I IlIl II III ll I 316 l I Ill~ lIIIoo/ cv- osy 2o1 · cv- -s 9- -osy 2o1 ... Subramaniam Rajan,...
Transcript of I IlIl II III ll I 316 l I Ill~ lIIIoo/ cv- osy 2o1 · cv- -s 9- -osy 2o1 ... Subramaniam Rajan,...
AD-A241 316 -. oI IlIl II III ll I l I Ill~ lIIIoo/ cv- -s 9- - osy 2 1
Predictions and Observations of Seafloor Infrasonic Noise
Generated by Sea Surface Orbital Motion
by
Timothy Edward Lindstrom ', (B.S., Electrical Engineering
Rochester Institute of Technology (1978)
Submitted in partial fulfillment of therequirements for the degree of
OCEAN ENGINEER
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
and the
WOODS HOLE OCEANOGRAPHIC INSTITUTION
September 1991
© Timothy Edward Lindstrom, 1991
The author hereby grants to MIT, WHOI and the U.S. Government permissionto reproduce and to distribute copies of this thesis document in whole or in part.
Signature of Author ................ . .-Joint Program in Oceaorpi Enieering
Massachusetts Institute of TechnologyWoods Hole Oceanographic Institution
R A August 9, 1991 _Certified by ........................ A ............. .. .............
Dr. George V. Yrisk m
Senior Scientist _ N)oods Hole Oceanographic Institution
Thesis Supervisor CCertified by..... . ... . ....
C ertii ed y ....... ...P rofessor H en rik S ch m id tAssociate Professor
Masshusett h.nstitute of Technologv
Accepted by ................Dr. W. Kendall Melville
Chairman, Joint Committee for Oceanographic EngineeringMarsachusetts Institute of Technology/ Woods Hole Oceanographic Institution
91 10 4i O .*
Predictions and Observations of Seafloor Infrasonic Noise
Generated by Sea Surface Orbital Motion
by
Timothy Edward Lindstrom
Submitted to the Massachusetts Institute of Technology/Woods Hole Oceanographic Institution
Joint Program in Oceanographic Engineeringon August 9, 1991, in partial fulfillment of the
requirements for the degree ofOcean Engineer
Abstract/
/ A model is developed for the prediction of the seismo-acoustic noise spectrumin the microseism peak region (0.1 to 0.7 Hz). The model uses a theory devel-
oped by Cato- [J. Acoust. Soc. Am., 89 , 1096-1112'(1991)\f 0r an infinite depthocean in which the surface orbital motion caused by gravity waves may produceacoustic waves at twice the gravity wave frequency. Using directional wave spec-tra as inputs, acoustic source levels are computed and incorporated into a morerealistic environment consisting of a horizontally stratified ocean with an elasticbottom. Noise predictions are made using directional wave spectra obtained fromthe SWADE surface buoys moored off the coast of Virginia and the SAFARI sound
propagation code, with a bottom model derived using wave speeds measured inthe EDGE deep seismic reflection survey. The predictions are analyzed for noiselevel variations with frequency, wave height, wind direction, and receiver depth.
These predictions are compared to noise measurements made in EOONOMEX us-ing near-bottom receivers located close to the surface buoys. Good agreement isfound between the predictions and observations under a variety of environmentalconditions. --
Thesis Supervisor: Dr. George V. FriskSenior ScientistWoods Hole Oceanographic Institution
2
Acknowledgements
I would like to thank a number of people whose help madc this work possi-
ble. Foremost on this list are my thesis advisor, George Frisk, my co-advisor,
Subramaniam Rajan, and my MIT advisor, Henrik Schmidt. These three were
truly instrumental in the successful completion of both my course of study and
my research, and are greatly deserving of my gratitude.
This particular thesis would not have been possible without the ECONOMEX
and SWADE program support provided by the Office of Naval Research. Addi-
tionally, a great many individuals contributed directly to the sucess of these two
experiments and to my understanding and data acquisition efforts. Among those
at WHOI, I woulJ like to especially thank Paul Boutin, John Collins, Jim Doutt,
John Hallinan, and John Kemp. Those at other institutions who greatly aided
my work include Steve Elgar, Hans Graber, and John Shnelder. I would also like
to thank Mike Purdy and Steve Holbrook for providing me with the EDGE data
so soon after it was analyzed.
I will also be forever indebted to Eddie Scheer and Randy Richards for their
help in my titanic struggle with the computer.
Finally I would like to acknowledge Captain Frank Lacroix, USN, whose pro-
fessional guidance made it possible for me to become part of the Joint Program;
and my wife Cindy, whose love and support made it all worthwhile.
Wr.B i Ti I ~ i7
L&A tJ. 'J1 e '-\J -r0
3v& os 3
Contents
I IntreductICOn 6
2 Basic Equations 9
3 Solution to the Inhomogeneous Wave Equation 13
4 Application to Orbital Motion in the Deep Ocean 21
5 Prediction Techniques 32
5.1 SWADE data .............................. 32
5.2 Coupling factors and bottom gain ................... 38
6 Predictions for Receivers at 450 meters and 2500 meters 42
6.1 Variation of spectral level with frequency (spectral shape) ..... 42
6.2 Variation of spectral level with wave height ............. 44
6.3 Variation of spectral level with changing wind direction ....... 46
6.4 Variation of spectral level with receiver depth ............... 47
7 Experimental Noise Measurements 49
7.1 Experimental description ....................... 49
7.2 Data selection and processing ..................... 51
7.3 Observed results and comparison with predictions ........... 52
7.3.1 Spectral shape and overall spectral noise levels ......... 52
4
7.3.2 Variation with wave height.............................. 52
7.3.3 Variation with changes in wind direction ................. 54
8 Conclusions and Recommendations for Future Research 55
8.1 Conclusions................................................. 55
8.2 Recommendations for future research.......................... 56
Bibliography 58
Figures 61L
5
Chapter 1
Introduction
Researchers have long been aware of a peak in both the seismic ambient ground
motion spectrum and the ocean bottom pressure spectrum which occurs with a
period of about three to four seconds. This peak has historically been called the
microseism peak. It has been noted that the frequency of this peak seems to occur
at twice the frequency of the peak in the surface gravity wave spectrum. Longuet-
Higgins [11 was the first to develop a comprehensive theory which proposed the
interaction of opposing surface waves, which closely approximate standing waves,
as the source of the microseism peak. He showed that while the first-ordar pressure
fluctuations caused by the gravity waves exhuiit an exponential decay in depth,
the second-order fluctuations caused by the nonlinear interaction of two opposing
waves does not attenuate. Brekhovskikh [21 was the first to develop this idea into
a prediction of noise in the ocean. He has been followed by others, most recently
Kibblewhite and Wu 131, who all used a perturbation expansion as the solution
to the wave equation with the resulting second order solution as the acoustic
field. Cato 14] has developed a model which does not rely on a perturbation
expansion, and does not require that a standing wave approximation be made.
His theory predicts somewhat higher noise levels for a shallow receiver than those
using the perturbation expansion, and a different directionality. In contrast to
6
these predictions, which have the wave interaction as the source mechanism, are
those of Guo 151 who has proposed the wind turbulence acting on the surface
directly as the source of noise in the microseism peak region.
Previous measurements of noise in the deep ocean have been few, and the re-
sults have been broadly consistent with all the above theories [6,7,8,9]. What has
been lacking is a direct accurate measurement of the source field believed to be
causing the noise, either the wave field or the wind field. Without these quality
source data, broad assumptions concerning the source field must be made, and
the potential variance in the predictions based on these assumptions are typically
greater than the differences in levels predicted by the different theories. Thus
without the accurate measurement of the source field, it is difficult to evaluate
the adequacy or inadequacy of particular theories. In the case of the surface
wave field, the required measurements consist of directional surface wave spectra.
This lack of high-quElity, simultaneously measured, noise and surface wave data
was the primary reason for the deployment of the ECONOMEX and SAMSON
e xperiments [10,11]. An additional desirable feature of the ECONOMEX experi-
ment was its long-term nature, allowing noise measurements under a wide variety
of environmental conditions. The measurements consisted of near-seafloor water
pressure and ground motion at various depths from -100 meters to 2500 meters
in the Atlantic Ocean. During the time the ECONOMEX instruments were de-
ployed, instruments in the same area from the SWADE program were measuring
surface parameters including directional wave spectra, wind speed, and other me-
teorological quantities. These two coupled data sets provide researchers with the
measurements needed to test the theories mentioned above.
This work will examine the model developed by Cato [12] for an infinite depth
ocean and will present the derivation of that model in detail. Using the SWADE
directional wave spectra as inputs, we will estimate the resulting acoustic source
level. We will then incorporate this source level into a more realistic environ-
7
ment consisting of a horizontally stratified ocean with an elastic bottom using the
SAFARI program [13,14]. The geoacoustic model for our bottom comes in part
from the EDGE deep seismic reflection study [15]. The resulting ambient noise
predictions will then be compared to the measured noise from ECONOMEX in
an effort to judge the adequacy of our model.
In Chap. 2, we review the equations of motion and derive the inhomogeneous
wave equation in terms of the Lighthill analogy [16]. The inhomogeneous wave
equation is then solved in the presence of a sound speed and density discontinuity
in Chap. 3. In Chap. 4, we make some simplifications to allow us to apply
the theory to the motion of surface gravity waves. Additionally in this chapter
we follow the work of Cato [12] in deriving an expression for the noise level in
terms of the directional wave spectrum, a problem for which we also introduce
an elastic bottom. In Chap. 5 we describe the methods used to make predictions
of noise levels using the equations in Chap. 4, the SWADE directional spectra,
and the SAFARI program. Finally in Chap. 7 we present the ECONOMEX noise
observations and compare them to our predictions which, for the most part, agree
very well. Our conclusions and recommendations for future research are presented
in Chap. 8.
8
Chapter 2
Basic Equations
In any consideration of sound generation, the most basic question to ask is "What
is sound?" That is, how do we distinguish particle motions associated with acous-
tic energy from that associated with other types of energy such as vortical energy
(that due to turbulence) or thermal energy? In general, this is a very difficult
question, for the equations governing the three types of motion are a set of cou-
pled, inhomogeneous, non-linear partial differential equations, first derived in a
linear form by Rayleigh [17], and later in a more general form by Doak [18]. Doak
further showed that for small Stokes number the set decouples into three separate
equations for the acoustical, vortical, and thermal type motions. For our model
of sound generation, we will consider only this decoupied, small Stokes number
approximation, and introduce any coupling between the three types of motion via
external forcing, heat addition, or boundary conditions. The acoustic motion is
then easily recognized as the small scale pressure perturbation associated only
with the internal elastic properties of the medium.
Let us consider the validity of the small Stokes number approximation in the
case of low-frequency sound in the ocean. If we limit our interest to a maximum
frequency of 50 Hz, then the maximum Stokes number (wv/c 2 ) is ; 10 - 7 , where w
is the acoustic frequency, v is the medium viscosity, and c is the sound speed. We
9
are then justified in using the assumption of small Stokes number and can take
advantage of the great mathematical and conceptual simplifications it allows.
In our derivation of the sound generated by a moving fluid, we will follow the
acoustic analogy method of Lighthill [16], but will use the pressure perturbation
as our field variable in preference to fluctuatinns in mass density as suggested by
Doak [18]. We will first derive an expression for the pressure perturbations in an
ideal acoustic medium at rest, and then derive a similar expression for a real fluid
which may contain variations in density, variations in sound speed, and which can
have existing within it any type of motion. When we compare the two expressions,
the difference will contain the effects of motion in the red fluid which generate
sound.
The exact equations of mass conservation and momentum can be written as
ap +(pu,) 0, (2.1)
d(pu,) + + -p+, - 0, (2.2)7i axj
where p is the was. dsity, uj is the fluid velocity in the xi direction, aij is the
stress tensor consisting of hydrostatic and viscous stresses, and fi is the body
force in the xi direction. The indices i and j may take any value 1, 2, or 3,
corresponding to the Cartesian coordinate axes, and a repeated index i_" -torm
indicates the term is to be summed over all values of the index.
If we consider the "acoustic approximation", p - Po = c0, 2(p - p(), where p is
the fluid pressure, then Eq. (2.1) can be rewritten
1 ap a(pui) = 0. (2.3)Coi -act + -axi
Doak has shown that this approximation is exact for an inviscid, non-heat con-
ducting fluid, and valid for a Stokesian fluid to first order in the Stokes number.
10
Equation (2.2) can be applied to our ideal acoustic medium by linearizing it and
neglecting viscous terms, leaving
a(pui) p_S + 0=. (2.4)
We can now combine Eqs. (2.3) and (2.4) by eliminating pui to yield
atV P 2 2 = 0. (2.5)
This, then, is the familiar homogeneous wave equation governing the pressure
perturbations in an ideal acoustic medium.
Now consider the exact equation of momentum balance, Eq. (2.2). This can
be expanded asa(p,,) ap a(Pu, + + Ph , (2.6)
where S is the viscous stress tensor, and the hydrostatic term has been explicitly
stated. Next we again eliminate pu by using the exact equation of mass conser-
vation, Eq. (2.1). By adding a2p/aza to both sides to allow direct comparison
with Eq. (2.5), we arrive at
a2p _ a2p 2 a 2(pu, + S,,) +a2 (p c~p) a(pf,) (2.7).t----0 =z p + -2 (o27
This is the inhomogeneous wave equation as derived by Doak [18]. It is iden-
tical to that derived by Cato [41 with the exception of the final term, which he
neglected. The pressure fluctuations in a real fluid are exactly those which would
occur in a uniform acoustic fluid subject to the external stress system given by the
right hand side of Eq. (2.7). As c is assumed constant, not only the sound gener-
ation but also the propagation effects of a real fluid are included in the equivalent
stress system. It will be our task not only to solve Eq. (2.7) in an ocean geome-
try with a realistic stress imposed, but also to separate out the sound generation
terms from the propagation terms.
It is useful at this point to consider the importance of the term c2a(pf)/x,,
which was neglected by Cato in his theory of noise generated by surface orbital
11
motion [4]. In the ocean, this term reduces to cog(,9p/az). We will consider
motions with a periodic time dependence (p oc e -".t) and a characteristic length
scale L. Then we can form the ratio of the last to the first of the terms on the
right hand side of Eq. (2.7) as (gp/L)/(pu2 /L 2 ). From Eq. (2.1), we can see
IpU/L I -, wpj so we can rewrite our ratio as g/Lw2 . We can also see from Eq. (2.1)
that the first two terms on the right hand side of Eq. (2.7) are of the same order. If
we consider as our worst case a minimum frequency of 0.1 Hz, we can neglect the
gravity dependent term if L > 25m. If we were concerned with purely acoustic
motion, the appropriate length scale would be the wavelength L = A "- c/f -
15,000 m. However the length scale appropriate to the equivalent sources resulting
from surface gravity waves would be the wavelength obtained from the deep water
low frequency surface gravity wave dispersion relation w2 = 27rg/A which yields
L = A - 160 m. In both cases we can therefore neglect the last term in Eq. (2.7).
12
Chapter 3
Solution to the Inhomogeneous
Wave Equation
The general solution to the inhomogeneous wave equation is well known (cf. Strat-
ton [19]). For the source term in Eq. (2.7), it is given by
p(x,t) Po =
f[82 (pU,,+ si). a 2wpc-,p) dy4rv[ + at2 Jt -y, aa-r
+ ifsa-a p r larapj dS(y), (3.1)
where r = Ix - yl, A is the outward normal to the surface of integration, and
the integrands are evaluated at the retarded time r = t - r/c. The volume of
integration above must include all possible regions where noise could be generated,
and the surface integral will include the boundaries of these regions. We will choose
our volume to be a cylinder of infinite height above the sea surface, and extending
to the ocean bottom. The radius of this cylinder Y is assumed to be large enough
to include any regions of motion which could contribute to p(x, t), and thus the
sides of the cylinder do not contribute to the surface integral. We next follow
13
Cato 141 in modeling the sea surface density discontinuity as a Heaviside function
so that the derivatives in Eq. (3.1) exist. The density is given by
p =- H(x - )(p. -P p) + Pa
where pg, is the density in water, p. is the density in air, is the value of x at the
interface, and B (x - ) is the Heaviside function
H(y) = 0, y > 0,
H(y) = 1, y < 0. (3.2)
We can then expand terms containing spatial derivatives of p as follows:
a2(p,,)-
ayiay,
82 0
H ay, ( )t+ y, (pyatituj)
-( p 4)tuu + (p1, - • 1 H. (3.3)+2y, Oy, P auu p - p.)t uuij.
We can also combine Eqs. (2.1) and (2.2) to yield
a2= a2(pu, + a'j) (3.4)
which can be used with Eq. (3.3) to eliminate the derivatives of the Heaviside
function in Eq. (3.1) resulting in
41r(p(x, t) - P0) =
-ILy [Hla8 (pLuj) + (1- H) a2(Pauj) + ap
+[1H H) - (p,u,) + 2 -2)]
[l8p+ 1 Or +1 8r Op1+1 a -- +---p+--- I dS(y). (3.5)
Jsr rn ra8n 0 ~n T
14
Now we can split the volume integral into one integral over the water volume
and one integral over the air volume, noting that H = 1 in water and H - 0 in
water, and after recombining terms to form 82p/at2 we find
4PUiui + S.) + p0- P.)
+ y [a (p..,u, + + 2 (p
t+f , -a " ) + pa )
fS[lop 1lr Or Op ] ) (3.6)
r , + - + ;72 o- dS(y). (3n)
As before, the integrands must be evaluated at time r = t - r/c
The next step is to apply the divergence theorem in a manner first described
by Curle [20], and presented in detail by Cato [12]. This is not a straightforward
process, as the terms to be evaluated depend on y both directly and also through
the dependence on i-. Curle stated and Cato demonstrated that
f1:2? d dy _ 1f~vay, ayj r- ax, v ay r royi t yj rJ d
-f l dS(y) (3.7)• scyj r'
where Ii are the direction cosines of the outward normal of the surface enclosing
V. We can then repeat this operation a second time to yield
SdS(y) (.
v ayj r Jo'i 38
We can now combine Eqs. (3.8) and (3.9) to achieve Curle's result
f 82 F,,dyv ayjj r
a 2 . f .dy af Fidy + !.F'./dS (y)+ Ffj 1,F. + i (3.9)
i5s r s 'yj r
15
We can also easily transform the surface integral in Eq. (3.1) as follows. First we
resolve the normal derivatives into Cartesian coordinates which yields
fs [ 1p 1 r 1 r p](y[. ri ap 1 r 1 ar api dS(y). (3.10)
By substituting ar/8yi = -ar/ai and ap/ala = a(pb6)/1yj, we have
f li [ 1 ar [!1 ar dS(y)]sl [r-'yi-r2-ylp + -or jy-'a .rSY
/fla(pjj) dS(y) I [1 ar 1 ar api dS(y) (311)--ay js ai + -j- (3.11r
Next we note that
a [f(t ) 1 f ,f]ar
so that we can write
a(pbq) dS(y) [1 ar 1 a r a dS(y)
- fa ' p dS(- y)r (3.12)
Combining Eqs. (3.10), (3.11), and (3.12) yields[1 OF 1r i a::r a:p] ds(y)=
f/s [rtnap + " anp + r an t J,Is [!f S,+ )dS~y)+
s ay, r aslil- dS(y) (3.13)
Now we substitute Eqs. (3.9) and (3.13) into Eq. (3.5). After noting that the
source motions at infinity do not contribute, we can separate the surface integrals
enclosing the water volume into one at the air-sea interface designated S and one
at the ocean bottom designated Sb, and can then combine the surface integral at
16
the bottom derived by aPplying the divergence theorem to V., with the surfaceintegral of Eq. (3.13). This yields
47r(p(X, t) - PO) =
a2~x, (P.Uiui , d + a2 (p(5- 02 p dy
+ f1, Pauiu + SA +rV±& d
a +aq dS(y) (.4
(2.2 thati[5f,4 G~~ + S + P6.AJ =Sy
0 ~ 08 J(Pwuii±Sq) +xi r1*r
+ O+j+,'I(vWi j+2(cpbj)
a r dSy)] dS (y) ~ y+i + ISP8, ~ u.
aw7r
We ca t a sf rm t e d ri aiv s oti e eiv ti esb n ti g frm7q
+- 1(-UF + S~i + AAi dS(y)aT
f 1' dSdSy)axJi~Puu s, +5 r
+ sl-( P . U ) dS(y) (3.15)
We can now begin to interpret the meaning of Eq. (3.15) in terms of the sources
of classical acoustics. The double spatial derivatives of the volume integrals are
recognized as distributions of quadrupole sources in the volume V, and the single
spatial derivatives of the volume integrals are recognized as dipole source distri-
butions in the volume V. The spatial derivatives of the surface integrals at the
interface are seen as dipole sources caused by the motion of the surface of the
density discontinuity, and similarly the surface integrals of the time derivatives
are seen as monopole source distributions caused by the motion of the surface of
the density discontinuity. These interpretations are those given by Lighthill [161.
In order to interpret the terms involving the double time derivatives, we must
make a further approximation to allow us to simplify Eq. (3.15), although it is
one that is frequently made in classical acoustics. If we assume that the fluids are
isentropic, then the density and pressure are simply related by ap/ap - c2 , where
c is the local speed of sound 1211. Also, if entropy is conserved, the processes
are reversible and the dissipative effects of viscosity can be ignored. (Note we
must now treat the effects of attenuation due to absorption separately.) With no
viscosity, S = 0, or aij = P6bi. We can thus write
or using Eq. (3.4) we have
t2 C22p t
c 2 a 2(
2 )(puu + ai)] (3.16)
18
We can again apply the divergence theorem twice to Eq. (3.16) to yield
a2 L y
a2~z J (C2 - PUitLj+ p(5j) da ( 2 r d
a C 2 _ 1) (puj + pb6 j)+ \ci J r
ax-p -(4
a [(C2 _ 1) PU] ,y)* (3.17)
From the above, we note that we can again identify both a quadrupole and a
dipole volume source distribution, and both a dipole and a monopole surface
distribution. Next we combine Eqs. (3.17) and (3.15) resulting in
4ir(p(x,t) - P0) =
~ Iv, [(P.oUiUj + P8a2- V [ 2 Idy+ I 1j (PatiU,+p6,) _ p6,, raxaz, i. q I
a tF,2 d c2-y Sy
a ,-. (p",uu, + p,) - pi
aai . CO r
1 1a
I a [(p.C2 _ ., Sy)-t- -I,, - ( p ' ' ) U, +. (C p6,j),
2Ca dSw Syy
-f Sl, ( (op.U,) (3.18)
This result shows that the sound received at a point is the sum of apparent
sources distributed throughout the source volume, at the air-sea interface, and at
19
the ocean bottom. The effects of the real ocean, such as refraction, are included
in Eq. (3.18). The reflection from the ocean surface and bottom are also modeled
in Eq. (3.18). Our next step will be to further simplify Eq. (3.18) to identify the
real sources which transform other types of energy into acoustic energy, and to
show how the sound generated by these real sources is modified by a homogeneous
ocean.
20
Chapter 4
Application to Orbital Motion in
the Deep Ocean
Equation (3.18) is quite general and could in theory be used to predict the acoustic
pressure for a given source mechanism, but would require a knowledge of the
particle motions ui throughout the volume of the ocean and on the boundaries.
In addition, the effects of a real fluid such as refraction are modeled as apparent
sources, which further confuses the issue. We will now begin to make assumptions
which will greatly simplify Eq. (3.18) to allow us to use it to predict infrasonic
noise generated by the sea surface orbital motion.
We first assume a plane wave sea surface elevation
= acos(e • xi - at), (4.1)
where C is the sea surface elevation, a is the amplitude, r is the wavenumber
vector, x = z- + z 23 is the horizontal position vector, and a is the radian gravity
wave frequency. The solution to the linear equations of motion yields a velocity
potential 0 at depth z 3 - z given by
aa cosh (z + d) sin(.- x' - at), (4.2)
r. sinl rd
21
where d is the total water depth and r. = I 122]. Ignoring surface tension, this
leads to the dispersion relationship
a2 = gitanhcd, (4.3)
where g is the gravitational constant. If we restrict ourselves to water deep enough
to satisfy red > r/2, Eq. (4.3) reduces to the deep water surface gravity wave
dispersion relationa2 = r. -(4.4)
We then find the particle motions to be
x = aer-Osin(e.- ot), i =1, 2,
z = aer cos(x . - ot), (4.5)
where the initial position of the particle is (x , z0). We can see that the particles
describe a circular path, and hence the term orbital motion. Now we must de-
termine the minimum water depth for which we may neglect the orbital motions
at the bottom. We will also need to find the minimum water depth for which
Eq. (4.4) holds. If we consider a minimum gravity wave fi equency of 0.05 Hz,
the deep water dispersion relationship is valid in water depths > 200m. To find
the depth at which we can neglect orbital motion on the bottom, we consider the
eC- decay with depth and we find the orbital motions are 5% of the surface value
at a water depth > 300m. We will therefore consider to be the effective source
generation region to be <300 m. Outside this region we may neglect the volume
integral of Eq. (3.18) and also neglect the orbital motions on the bottom.
We can eliminate any apparent sources caused by refraction by considering
the case of an isovelocity ocean, or c, = co, and by considering the air also to be
isovelocity, c. = F.-. We can also eliminate a number of terms in Eq. (3.18) by
noting that c 2 >~ C!and pc > p.C2. Thus, we neglect the air volume integral,
and we assume the upper half-space to be a vacuum. We have now reduced the
22
motions on the bottom to those due only to the motion of the acoustic wave.
Thus, in Eq. (3.18) we can eliminate from the bottom integral the puuij and
8(pu)/at terms, since for an acoustic wave pu < p. After all these simplifications,
we are left with
47r(p(x,t)- Po) 2 f -I dyazazjf, J~tLr
a Ii + dS(y)
9zJ,' +i rh
+ fS, a-[P ui ] dS(y) + & f l1 P6 i'dS(y) (4.6)
One can now identify each term in Eq. (4.6) and relate it to a specific physical
mechanism. The quadrupole volume integral involving pu iui is identified as the
volume contribution to the second order pressure fluctuation first proposed as
the cause of microseisms by Longuet-Higgins [1] . The dipole surface integral
involving puju, is identified as the sea surface contribution to this mechanism.
The monopole surface integral containing pu, is identified as the first orderpressure effect which attenuates with depth. The apparent sources due to the
surface and bottom reflections are contained in the two pbij terms . We can see
in this case that the bottom does not influence the real source terms directly, and
the real sources caused by the transformation of mechanical energy to acoustic
energy can be evaluated first, and the bottom effects added later.
Cato has shown [4] the quadrupole contribution to be < 2o/c times the dipole
contribution in the far field, which is defined by rx > 1. For a minimum wave
frequency of 0.05 Hz, this is then valid at depths greater than 100 m below the
region of effective volume generation, which we found to be no greater than 300
m. Thus we are able to ignore the quadrupole term for receivers greater than 400
m. Since we are mainly interested in the microseism peak region, we will also
neglect the monopole term, although it will be significant at moderate depths for
frequencies below the microseism peak.
23
In finding the acoustic source level, we must make two major calculations.
The first is to relate the source acoustic power density P(w, z) to the frequency-
wavenumber spectrum of the source motions puiu,. We must then relate this
spectrum, say 4(w, k), to O(a) which is the readily measured power spectrum of
the sea surface elevation . Both of these derivations have been performed by
Cato [4,12], and we will present the important steps for the dipole sources below.
We must then incorporate these source levels into an appropriate ocean model to
find the noise power for an ocean receiver.
We start by redefining some terms. Let
PD (x,t) = 'f1jG(r)Wi($,r)dy, (4.7)
where Wq = puu 3 , G(r) = 1/(47rr), and k is the source coordinate on the sea
surface. Since we will perform the integration over the mean sea surface, we can
immediately align the x3 axis with the depth axis z and then 11 = 12 = 0, 1s = 1,
and Wq = Wi = puius. We assume Wi to be temporally stationary and ergodic,
and spatially homogeneous. Then the autocorrelation function of PD (x, t) is
Rv(t,t + q) " ((PD(X,t)PD(x,t + ')), (4.8)
and since the process is ergodic
R,(t +;)= () = lim f fT pD (Xt)pD (xt + -;)dt, (4.9)T-.c 2T
and the power spectrum is
QD(w) = HiMf T pD(X,t)pD(X,t + -)dt ew d
- p1 fT fAjC(r)Wi(k'r)dk]
x a f G(r')W,(y', r')dkI dt e"'; d,. (4.10)
24
Since :V and ' are independent, we can define a separation parameter q in a cross
correlation function of W
Rw,, = l ft)w 1 (S" + ,t + ;)dt, (4.11)T--+ooT -T
and we can further define the cross spectrum of Wi
Cl(,"= Rwi,,(,, ) ' d,. (4.12)
We also note that
6,(1(q,w) = f jj(w,k)eikr (2)2 (4.13)
Finally we can combine Eqs. (4.10)-(4.13) and after making some substitu-
tions, find that
Q0(w) = (w,k)Hi(wk,z)H, , dk (4.14)
where
H,( w,k,z) = •---k a (e'- k f e-i(wr/c+kt) ) (4.15)
This completes the first step in determining the source levels from surface
orbital motion. We have the source level QD as an integral of the wavenumber-
frequency spectrum of the orbital motions times the coupling factors HiH*. Cato
has calculated Hi analytically for an infinite ocean radius, and the values can be
calculated numerically for a finite ocean radius [4]. Cato provides a thorough
discussion of the behavior of the coupling factors [4] and has shown the spatial
dependence of the coupling factors to be
Hiocexp-i[k.-+ zV(010) k2]}. (4.16)
One can see that the spatial dependence is entirely oscillatory in the horizontal
direction, but is oscillatory in the vertical only for k < w/c. For k > w/c the
25
coupling factor magnitude has an exponential decay with depth. This will lead to
an important approximation later in the development.
Cato has also provided a convenient form for the coupling factors in terms of
dimensionless quantities M = w/kc, X = xaw/c, Xo = Rw/c and A = zw/c:
Hi (w, k,z ) = -i cos Ho(w, k, z) /M,
H 2(w, k, z) = -isincrHo(w,k,z)/M,
_a
Hs(w,k,z) = 5AHo(w,k,z), (4.17)
where a is the angle between k and the Yi axis, and Ho is the monopole coupling
factor1 fX0 Xei 'X+ A2
Ho(w,k,z) = 2 A2Jo(X/M) dx, (4.18)
JO being the Bessel function of the first kind, order zero.
We must now relate the frequency-wavenumber spectrum 6jj to the surface
wave height power spectrum fl. We start by relating the spectrum of ui to that
of puiu,. Cato has shown [12] that
Pimj,,(w,k)/p 2 = Tii(w,k) * 'j',.(w,k) + qim,(w,k) * TiL (w,k), (4.19)
where * denotes convolution and T 1 (w,k) is the power spectrum of uj. We can
expand one of these terms in polar coordinates, with a being the gravity wave
frequency, as
It,,m(w, k, a)], = p2 E 0 ,=ro .. _1 0 ,0,,)
d - d'-ydcaX Tj' -ga, (27r) 3 (4.20)
where i' = k - r, with -1, -y' being the angles x, ' make with the yj axis. We can
define a' = w - a, and can now identify a and a' as the frequencies and X and X'
as the wavenumber vectors of the two interacting waves ujuj, and w and k as the
resulting acoustic frequency and wavenumber. We can relate the wavenumbers
26
and angles by
kcosa = iccos-y+Kr'cosy',
ksina - I sin-y+c.'sin"y'. (4.21)
Since o and r. (and or' and ic') are associated with the orbital motion of surface
gravity waves, they are uniquely related by Eq. (4.4). This is not true for w and
k. We can, however, use the behavior of the coupling factors previously described
to find approximations for w and k in terms of a and tc.
We will again follow Cato [12] in noting the exponential decay of the coupling
factors as k exceeds w/c, and we can choose a value 6 such that we will only
consider a Fourier component to ensonify a region if k < fw/c. From Cato's
examination of the coupling factors [4], we can choose 1 = 5 for a practical
receiver depth. We can now write
- P1w/c < IkI _ 13w/c, (4.22)
but Iki > jr1 - [x j so we may use the deep water dispersion relationship to write
- w/c < /'g - (w - o)'Ig __ ,w/c, (4.23)
or
Iw - 2I -< O1/c. (4.24)
Thus, the acoustic frequency will be within 3% of twice the gravity wave frequency.
We can say with reasonable accuracy that
w 2-- 2a'. (4.25)
We now have formally obtained the frequency doubling effect, where two gravity
waves of the same frequency interact to generate an acoustic wave of twice that
frequency. We can similarly show that r = x.
Next we define the two-dimensional wavenumber spectrum of ui
=] %P(a,'KY) d. (4.26)
27
Since o and x are related, we can define b as the specific value of a determined
by Eq. (4.4). Also, since k and w are not variables in the convolution integral Eq.
(4.20), r.' = 1k - icr, and we have the two relations of Eq. (4.21), we can find K
and ' in terms of -y. We will define the values of a and ic thus determined as &,
and ir.. Now we will make the assumption that the two-dimensional wavenumber
spectrum is separable into a one-dimensional spectrum times an angular spectrum,
,,(i, y) -- 2i-xi(iv)G(o, )/v, (4.27)
where the angular dependence satisfies
G(o,) d-- 1. (4.28)
After substituting Eqs.(4.26) and (4.27) into Eq. (4.20), making the variable
substitutions mentioned above, and also substituting dr. = (av/ab) da, we note
that we can eliminate two of the three integrals in the convolution. Then
f4 ,ij i..(w , k ,a ) , = 2 7rp f X ()x m ( ,') G( , y) G( ',2r
1 0.x , r,( y d-. (4.29)
We arrive at a similar expression for the second term on the left hand side of Eq.
(4.19) by substituting subscripts. We can write the sound pressure spectrum as
QD(W) = f 27rp 2 f2Xiw()Xim(')
+ Xim(r)Xj,(r.')]G(a,-)G(a',y' )
X a 13-. dk (4.30)
Cato has shown that for significant ensonification of the noise field .,, rv!,, and
o, can vary by only a small proportion of their values, and thus can be regarded
as constants in the integration. Also, G(o, -y) varies relatively slowly, and . - i',
28
so we can substitute G(O, Y)G(a,'y + r) for G(o,'y)G(o', "y). We can differentiate
Eq. (4.5) to find
XII = cos 2 "̂ " Xss,
X22 = sin2 I' X3,
X1s = COS 7"X33,
X2s = sinI*x33. (4.31)
We further define the one-sided frequency spectrum of u3 as fl(or) and can write
A(0) = TX3s(c), (4.32)
and since u3 = at/at, we have the frequency spectrum of the wave height in terms
of the wavenumber spectrum
1 ax;fl(c) = ;'7--TX3(r-). (4.33)
We can now see that
Xa (r-) = g(-) nl(0) -ao-or2 , (4.34)
where gi, can be found from Eq. (4.31) and g33 = 1. We note that
gig(-)gs(- + 7r)ba = gis(-l)gs(Y + 7r) ,a, (4.35)
and so both terms of Eq. (4.30) are identical. We can then write the sound
pressure in terms of n(or),
QD(w) = 2p--f l(a& )I,() o I H l k kb 1 (4.36)K,' D0 Jo o 27r
where
= jo g,&Y)gss(-y + 7r)G(O,'Y)G(O,-I + 7r)di.- (4.37)
We can see that I= + 11 22 = .
29
Next we separate out the a dependence of the Hi, perform the a integration
of Eq. (4.36), and note that H, = H 2 to find
QD(W) = P 2&4a&n2 (&)I."(&) 0 I + 21 3 H) k dk, (4.38)
where Ai = fI (w, k, z). Finally, we use the dispersion relationship to substitute
IC' = cr4/g, o9/ic = g/(2&), and we use Eq. (4.25) to substitute = W' = w/2,
and we have the result
QD(w) = fgWf2- 2 (w/ 2 )Ia.(w/ 2 ) f0"(ih1 + 21'If )kdk. (4.39)
This gives us the received pressure for an infinite depth ocean in terms of known or
measurable quantities. We can measure f)(o) directly or use an empirical spectrum
based on wind speed. We can similarly measure or imply from the wind speed
G(a,-y) and thus calculate la33 (or). H,,H%* can be calculated for a given geometry,
and p and g are physical constants. We thus have an equation which will allow us
to predict the noise spectral levels for a receiver in an infinitely deep ocean.
We must now turn to the problem of finding the noise levels in a more realistic
ocean. We will consider the case of horizontally stratified media in the water
column and in the bottom. Schmidt and Kuperman have shown that we can
write the noise intensity generated by a horizontal distribution of homogeneous
sources at depth z as [23]
P (w, z, z') = q2(w, z) T' T (w, z, z), (4.40)
where q2(w, z') is the acoustic monopole source strength of the distributed sources
of order m, and we can call T the bottom gain:
TK(w,z,z') = K2 ) J lg(,z,z')j[K2 (z') - k'jkdk. (4.41)
In this equation K(z) = w/c(z), and g is the depth-dependent Green's function
satisfyingd2g 1dz- + [K 2(z) - k ]g = (z - z'). (4.42)
30
We can eliminate the depth dependence in q(w, z) by normalizing the source
strength to that produced by the same source distribution in an infinitely deep
ocean, Q(w), where to first order q2(w,z') = Q2(w)/162r(z') 2 . Now, provided z' is
chosen small enough compared to the wavelength, Eq. (4.40) is approximately in-
dependent of z', and we have only to find the equivalent monopole source strength
and evaluate T(w, z, z) to find P(w, z). While the solution to Eq. (4.41) for an
elastic bottom is not available analytically, there are numerical solutions available.
We can easily relate QD(w) to its equivalent monopole source strength by noting
from Eq. (4.17) that
HH; + H 2H; = HoHO/M 2,
H s H = C zHoH. (4.43)
Thus the combined horizontal components are of vertical order m = 1 and the
vertical component is of order m = 2. We can now write
PD(W) = [gf22 w2I.(1) x JT2w )Io HoHO/M~kA81r
+ T2(w,z)-fo HoHokdk] (444)
where the index on T indicates the order of the vertical model used in Eq. (4.41).
We now have the full solution to the received pressure spectrum in a horizon-
tally stratified ocean. We will next look at the specific techniques and data used
to generate predictions of the noise pressure spectrum
31
Chapter 5
Prediction Techniques
5.1 SWADE data
The SWADE project (Surface Wave Dynamics Experiment) was an effort to char-
acterize the sea surface using a variety of sensors and, at the same time, to measure
other relevant environmental parameters [241. The project included several pitch
and roll surface buoys, satellite radar backscatter measurements, SWATH ship ar-
ray deployments, and aircraft overflights. The long-term deployment of the pitch
and roll buoys is the element of the experiment of direct use to us in our effort to
predict noise generated by surface orbital motion.
SWADE and ECONOMEX instrument locations are shown in Fig. 1, and
the overall experimental schematic is shown in Fig. 2. Deployment locations of
SWADE instruments are listed in Table 5.1.
The buoys provided one complete set of measurements including a spectral
Instrument name Type Latitude Longitude Water depthDISCUS E Pitch and roll 370 20.0'N 73* 23.5'W 2670mDISCUS C Pitch and roll 370 32.1N 740 23.5'W 102mDISCUS N Pitch and roll 38* 22.1N 730 38.9'W 115m
Table 5.1: Relevant SWADE instrument summary.
32
estimate each hour, allowing us to update our estimate of the noise each hour.
The spectral data from the SWADE buoys was provided for frequencies from 0.03
Hz to 0.34 Hz in 0.01 Hz bins, allowing acoustic predictions from 0.06 Hz to
0.68 Hz. The SWADE buoys which were closest to the ECONOMEX instruments
were the Discus E and Discus C buoys. For predicting the noise at the deep
ECONOMEX site, the data of Discus E was used, while predictions of noise at
the three shallow ECONOMEX instruments were based on the data of Discus C.
The SWADE project had deployed a SPAR buoy near the shallow ECONOMEX
site with better angular resolution than the Discus buoys, but it sunk prior to the
ECONOMEX deployments. We should consider here the possible effect of using
a surface buoy moored in 95 meters of water (Discus C) on the predictions of
noise at the 450 meter and 790 meter OBS's. We can note from the measured
wave spectra that there is little energy below 0.1 Hz in the wave spectrum. If
we calculate tanh(kd) for the worst case of 0.1 Hz with d = 95 m we find our
dispersion relationship is in error by less than 1%. Thus we would expect no
correction need be made to our wave spectra measured at Discus C.
Let us now consider the angular resolution available from pitch and roll mea-
surements. Longuet-Higgins et al. [251 were the first to investigate the angular
response of these buoys as follows. If the wavelengths of the surface motion are
large with respect to the buoy diameter, the buoy tends to have the same motion
and orientation as the surface. Then if we measure the vertical displacement and
the two angles of pitch and roll, we will have three time series which represent
the vertical displacement , and its spatial derivatives c7/8zI and aC/z 2. Using
the notation of the last chapter, we may represent the sea surface as a stochastic
integral
= N fs exp(i(r . - crt))dS. (5.1)
Then, since x = (r. cos -y, r sin y), we can write our three time series denoted by
33
i, 2, Cas
, - Rf exp(i(c. z- -t))dS
R = fjii costexp(i( .z - ot))dS
fj iK sin-y exp(i(x . z - at))dS. (5.2)
Next we can form co-spectra C1i(a) and quadrature spectra Qiq(a) from the time
serios ,, Cj, and we find
cGn(a) = j F(ar -) dy,
C22(o) = I 2 Cos2 -yF(o, -1) d-,
c21(o) - f n2 siny F(o, ) dy ,
Qu,(o) = f cos'F(o,y) di,C23(or) = o" rx2coysin F(, -) d y,
Q1(a) = j sin YF (orq) d, (5.3)
where F(oyr) = fl(o)G(a,y) is the frequency-directional spectrum of the surface
elevation. We can define the Fourier coefficients of F(a, y) as
a,(o) + ib.(o) = _I enIF(a,-) d-, (5.4)ir0
where
F~ =ao + E [a, cos (n) + bn sin(nr). (5.5)n=1
We can see that the right hand sides of Eq. (5.3) are related to these Fourier
coefficients as follows:
1() 1 1,(a),
a 1Q12(a), bi(o) =1rk irk1 2
a2 = ( -0IC 2 2 (U) - Css(a)], b2(a) = 2rjC 2 s(a). (5.6)
34
The pitch and roll buoy then gives us the first five coefficients in the Fourier series
describing the angular spectrum of the surface elevation at each of the frequencies
for which we find the co-spectra and quadrature spectra of the time series. We
must now use these five Fourier coefficients to find estimates of the frequency-
directional spectra fl(a) and G(o,'y).
Our estimate of the wave power spectrum
fl(a) = f F(cy) = ,rao(o) = C,(,), (5.7)
is obvious from inspection of Eq. (5.5), as well as our definition of the co-spectra.
The best estimate of the directional spectrum is not as simple. An obvious
choice would be to try the truncated sum
= + -(a, cosY+ bsin-y+a 2 cos2-y+ b2sin2-). (5.8)
This sum is actually a convolution of the true directional spectrum with a weight-
ing function, and considerable smoothing results in the estimated spectrum. Cal-
culations of I, made using this type of directional spectrum estimate from simu-
lated directional spectra are typically in error by a factors of 103 . Other weighted
averages of the first five Fourier coefficients can be made, but they too produce a
much smoothed estimate.
Several investigators have fit empirical curves to measured directional spectra.
Longuet-Higgins has suggested the wave directional spectra fit the form [25]
G(,,y) o, I cos *(-y/2)1 (5.9)
where the spreading parameter a is a function of frequency and wind speed. Kib-
blewhite and Wu used an empirical relationship to find s based on the wind speed
and frequency, and then calculated ls analytically [3]. One could also match
the measured first five Fourier coefficients to the first five Fourier coefficients of
the empirical spectrum cos2 j -y/2 to estimate the parameter s, as suggested by
35
Longuet-Higgins [25], and hence calculate 'a8 3 . However, the data used to de-
velop the empirical formula are generally taken under conditions of steady wind
speed and direction. In our field data, the wind speed and direction can vary
significantly, giving rise to wave fields with different directionality, and in gen-
eral a broader directional spectrum than that predicted by the empirical formula.
Therefore, we would expect predictions of I., calculated from spectra derived
from empirical formulas to be lower than the true value under variable meteoro-
logical conditions. In particular, if the true directional spectrum is bimodal (two
peaks corresponding to two wave fields generated by winds in different directions)
there can be significant energy in opposing wave directions G('Y) G(y + 7) which is
not predicted by the cosine power curve. Donelan et al. have suggested a better
fit to the data is found in a sech l3-y distribution [261 with i3 being the spreading
parameter, but estimates of Ia based on estimates of / are also too small.
Another approach would be to use a data adaptive spectral estimation tech-
nique such as the maximum likelihood method (MLM) or the maximum entropy
method (MEM). The method used here to estimate the directional spectrum given
the first five Fourier coefficients is the MEM. This method produces a spectal es-
timate which retains the first five Fourier coefficients and estimates the remaining
coefficients based on the first five. We will follow Lygre and Krogstad [27] in
developing an algorithm to make this estimate.
We will define a function with a Fourier series (suppressing the dependence on
a) on the interval (-7r, 7r) as
D(y) = .- , CO = 1, - = cn. (5.10)2r noo
The entropy of D is defined by
H(D) = f log(D(-y))d, (5.11)
and it has been shown by Burg [28] that the function maximizing H(D) subject
36
to the constraint that the coefficients c,, equal some known ck for k <_ N is
( 1 02 (5.12)D()=27r 11 - Ole - i 'I -.. - Ne-iN'yDj 2 '
where 51 "'" -ON and 0, are obtained from the Yule-Walker equations
1 cj ... cN-1 1 Ci
X = , (5.13)
CN_1 "'" C1 1N CN
and0 ,2 =I j* 1 -Oc . . N C * v 5 1 4
In our case we have N = 2 with c1 = (a, + ibl)/ao and C2 = (a2 + ib2)/ao. We can
now solve this system of equations to find 4, in terms of cn:
01 = (Cl - C2C)/(1 - ICit2),
02= C2 - CII, (.5
and finally we can substitute these into Eq. (5.12) to find our directional spectral
estimate
1 - 4C; 2c; (5.16)= 21r1 - 41e-i* - ,02e2i, (51
We now have an estimate of the angular distribution of the wave energy at each
frequency which reproduces the first five Fourier coefficients which produced it,
and uses these and the Yule-Walker equations to extrapolate the remaining co-
efficients. This technique has been shown by Lygre and Krogstad [271 to give a
much more peaked distribution over the MLM technique, and to resolve a bimodal
wavefield.
Figure 3 shows the estimated spectra from the various methods for a simulated
bimodal spectral input, and Fig. 4 shows the estimates of directional spectra for
the 0.16 Hz bin from Discus E on January 27 at 1200. This datum was chosen as
37
illistrative because it occurs after a shift in wind direction, and one could expect
the true spectrum to be bimodal. One can see for the estimates from the simulated
data that the MEM estimate provides a better representation of the structure of
the actual spectrum. One can also note in the comparison of actual data a bimodal
structure is evident in the MEM estimate only.
5.2 Coupling factors and bottom gain
While the coupling factors f HHjk dk can be evaluated analytically for an ocean
of infinite radius, [41 they predict infinite noise when the horizontal components
are considered. We can solve this by adding a relaxation mechanism and thereby
attenuation in the water column, or we can use a finite effective radius with some
physical basis such as the ocean basin radius, storm radius (if applicable), or such.
The coupling factors must then be evaluated either approximately analytically or
numerically. The attenuation due to absorption at the frequencies of interest is
believed to be too small to limit the noise on ocean basin scales, and so we will
assume an effective radius. Calculations show that at distant ranges the horizontal
coupling factors vary roughly as i/k, and thus doubling the effective radius has
only a minor effect on the overall source strength Qir(w) .
Based on the distance to shore of the ECONOMEX deployments and on trans-
mission loss studies in this frequency range, an effective radius of 100 kilometers
was chosen. The magnitude of the coupling factors was then calculated numeri-
cally for receiver depths of 450 meters and 2500 meters. These results are shown
in Fig. 5.
The final step in making our predictions is the calculation of the bottom gain,
T,, for the horizontal and vertical components. The most computationally inten-
sive part of this task is the calculation of the depth dependent Green's functions,
g(k, z, z'), for which we use the fast field approach. The fast field approach can be
38
generalized to a fully elastic elastic media, but requires that the wave equation be
separable in depth, that is to say range-independent. We will use the fast field ap-
proach, that realizing errors that may ensue due to range dependent bathymetry
and media.
The tool used to solve the full wave problem in this work is the SAFARI set of
programs (Seismo-Acoustic Fast field Algorithm for Range Independent environ-
ments) developed by Schmidt and Jensen 113,141. The basic solution technique in
SAFARI is to represent the field in each of a series of homogeneous layers by the
Hankel transforms of the unknown potentials satisfying the homogeneous wave
equation. The boundary conditions at each layer interface yield a set of local
equations involving the unknown potentials of the adjacent layers. These local
equations are collected into a global matrix which can then be solved to yield all
the unknown potentials simultaneously. Solutions are determined efficiently by
implementing modern numerical techniques. An additional advantage relating to
this work is the inclusion of the integration of Eq. (4.41) as an option in the code.
The environmental model used in SAFARI requires a number of parameters.
The user must specify for each layer the compressional wave speed, shear wave
speed, compressional and shear attenuations, and density. The uppermost and
lowermost layers are taken to be semi-infinite half-spaces. Due to the long wave-
lengths involved at the very low frequencies of our predictions, the environmental
model should be as accurate as possible fairly deep into the bottom. It is fortu-
nate that compressional wave speed data from a deep seismic reflection study of
the U.S. mid-Atlantic continental margin was made available prior to publication.
The EDGE seismic experiment 1151 involved recording seismic profiles to 16 sec-
onds off the Virginia coast in the same region as the ECONOMEX and SWADE
experiments. Using the compressional wave speed data, the figures and equations
of Hamilton [291 and discussions with other investigators working in the area of
geoacoustic modeling [30,31], geoacoustic models were developed for the bottom
39
g layer depth (m) Cp (m/s) C. (m/s) -yp (dB/A) "7, (dB/A) Ip (gc7nYDvacuum * 0 0 0 0 0
fluid 0 1500 0 .015 0 1elastic 2500 1756 200 .5 1 1.8elastic 3165 2193 540 .3 .5 2.0elastic 3678 2495 895 .1 .3 2.2elastic 5011 2648 1314 .1 .3 2.4elastic 5276 3817 1900 .1 .3 2.7elastic 7231 4042 2011 .1 .3 2.8elastic 8896 6380 3180 .05 .1 3.0
Table 5.2: Deep site environmental model. Cp,, and "yp,, are compressional andshear wave speeds and attenuations, respectively; p is the density.
layer depth (m) Cp (m/s) C, (m/s) Ip (dBIA) -y. (dB/A) I p (g/cr 3 ) [
vacuum * 0 0 0 0 0fluid 0 1500 0 .015 0 1
elastic 450 1799 200 .5 1 1.8elastic 970 2174 540 .3 .5 2.0elastic 1396 2683 895 .1 .3 2.2elastic 2441 3441 1720 .1 .3 2.4elastic 3332 4398 1739 .1 .3 2.5elastic 4938 5872 2933 .1 .3 2.7elastic 6582 6159 3059 .05 .1 2.9elastic 8227 6380 3170 .05 .1 3.0
Table 5.3: Shallow site environmental model. Cp,, and -yp,, are compressional ,andshear wave speeds and attenuations, respectively; p is the density.
at locations corresponding to water depths of 450 meters and 2500 meters. The
models thus developed are given in tables 5.2 and 5.3. Depth profiles of com-
pressional and shear wave speeds at the two sites are given in Fig. 6. SAFARI
calculations of T2 for both m = 1 and m = 2 for a receiver at 450 meters and
2500 meters are given in Fig. 7.
We can obtain a qualitative understanding of the relative importance of the
different propagation mechanisms by looking at Fig. 8, contour plots of the magni-
tude of the wavenumber integrands plotted against the inverse of the phase speed,
40
or "slowness" k/w, and frequency. One can see for the deep site the normal modes
play the predominant role in propagating the surface noise to the deep receiver,
as only for the lowest frequencies do we get a contribution from waves with phase
speeds less than 1500 m/s. In the shallow case there is a significant contribution
at all the frequencies of interest from the lower phase speeds, indicating the im-
portance of interface waves. These waves are propagating horizontally but suffer
an exponential decay in the vertical, and thus they are excited only in the shallow
case.
We can combine the effects of the coupling factors and the bottom gain, along
with the constants in Eq. (4.44) to find the temporally invariant part of the
solution, and we can write our prediction as the one-sided sound pressure spectrum
level (dB re lAPa2/Hz)
SL(f) = 20log fl(f/2) + 10 log I.(f) + 10 log B(f), (5.17)
where f is the acoustic frequency f = w/(27r) and B(f) is this time invariant part:
10logB(f) = 197 + 10 log [f (T(f)foHoH /M'kdk
+ T2(f)f HsHkdk)]. (5.18)
The quantity 10 log B(f) is shown in Fig. 9 for both the deep and shallow sites.
41
Chapter 6
Predictions for Receivers at 450
meters and 2500 meters
S.1 Variation of spectral level with frequency
(spectral shape)
Since the wave height power spectrum appears in Eq. (4.19) as 12(f/2), we might
expect the shape of the acoustic spectrum to be related to the shape of the wave
height spectrum at double the wave frequency, but we will see this shape is mod-
ified by a number of factors. The wave height spectrum generally shows a very
steep rise to a spectral peak followed by a somewhat gentler (c or- 4) slope at
frequencies above the peak [261. This peak frequency is generally characterized as
being inversely proportional to wind speed, and thus is usually lower in frequency
at higher wave heights. The peak tends to be quite narrow, normally occurring
at frequencies of about 0.1 to 0.2 Hz, although in a newly developing wave field
it can be higher. This tends to give rise to an acoustic spectrum with a peak in
the 0.2 to 0.4 Hz range.
This overall shape will of course be modified by the effects of the directional
42
spectrum, the coupling factors, and the bottom gain as functions of frequency.
Effects of the coupling factors are easily seen in Fig. 5 and tend to emphasize the
higher frequencies, which will tend to mitigate the slope of the peak in the acoustic
spectrum at frequencies above the peak. The spectral slope of the coupling factors
is oc w2. The bottom contribution to the spectral shape is more complicated, as
seen in Fig. 7. In the shallow case, a peak in the bottom gain appears at about
0.18 Hz, which sharply drops to a low at about 0.28 Hz, and follows with a rise
above 0.28 Hz with a slope of about w. This will tend to flatten the acoustic
spectrum if the peak in the wave spectrum occurs above 0.1 Hz (as it almost
always does). The peak in the bottom gain at 0.18 Hz is normally well overcome
by the sharp drop in the wave height spectrum at wave frequencies below 0.1 Hz.
In the deep case, the peak in the bottom gain occurs at about 0.24 Hz, and is more
likely to have an effect on the shape of the acoustic spectrum. In most cases, the
frequency of this peak in the bottom gain falls slightly below twice the frequency
in the wave height spectrum, thus serving to broaden the peak in the acoustic
spectrum. Above 0.3 Hz the bottom gain is relatively flat in the deep case. Thus
in the deep location the bottom will tend to enhance the peak in the acoustic
spectrum, and at frequencies above the peak the down slope should be greater at
the deep location than in the shallower case. When we look at the overall transfer
function B(f) shown in Fig. 9, we see for the shallow site a post peak slope of
oc w3 and for the shallow case a slope of oc ws.
By far the greatest effect on the shape of the noise spectrum next to the wave
height power spectrum is the behavior of I., If one examines the behavior of
the empirical models, it is clear that the value of the spreading parameters a or
P vary such as to reduce the value of I, at the frequency of the spectral peak.
Mitsuyasu et al. [321 have proposed a model for frequencies above the spectral
peak in which a varies as 8 c (U/ga) 2 5 , where U is the wind speed. In Donelan's
model, P is dependent on a/p only, with a, being the frequency at the peak [26].
43
Variation of I... versus frequency for this model is shown in Fig. 10. One can see
that for either of these empirical models the directional spectrum is narrower near
the peak frequencies, and broader away from the peaks, and thus the spreading
integral I... will be a minimum near the peak. The effects of the wave height power
spectrum and the spreading integral will oppose one another, and again tend to
flatten the spectrum. We can see in Figs. 11- 26 the estimates of 10 log P(f),
fl(a/27r), 20 log(fl(f/2)), and 10 log I.. (f) for several illustrative examples for a
2500 m receiver, and in Figs. 27 - 30 the same quantities for a 450 m receiver. One
can see from Figs. 11- 30 that the wave height power input can vary by as much as
60 dB in a given spectrum over the frequency range, whereas the spreading input
varies over a much narrower range of up to 20 dB in a given spectrum. This Will
cause the wave height power spectrum to dominate, giving rise to a spectral peak,
although one much diminished from the peak in the generating wave spectrum.
In summary we find the shape of the acoustic spectrum will in general resemble
that of the generating wave spectrum in that their will be a sharp rise to a spectral
peak, but in the acoustic spectrum the peak will be of a lower magnitude and
broader than that present in the wave spectrum.
6.2 Variation of spectral level with wave height
The variation in the predicted noise with wave height will be the result of the
combined effects of the wave height spectrum squared and the spreading integral.
We saw in the last section that the two effects opposed one another, with the
variation in the wave height spectrum dominating, giving rise to a spectral peak.
When we look at predicted spectra from different times corresponding to different
meteorological conditions, we find the variation in the wave height spectra is again
greater than that of the spreading integral. We would thus predict an increase in
noise level with an increase in overall wave height or sea state, with the increase
44
in wave height again partially offset by the decrease in the spreading.
To allow us to see the effects of increasing wave height on our predictions,
it is best to study a period of relatively constant wind direction with increasing
wind speed and corresponding wave height. This will minimize the effects of
other conditions which could effect the wave directional spectrum, such as wind
direction versus fetch direction, sharp changes in wind direction, etc. We can see
from Fig. 31 that we have such a time available to us at Discus E from 0300 to
1200 on January 21, 1991. During that time, wind speed rises from about 5 m/s
to about 12 rn/s with a rise in significant wave height of 0.25 m/s to 1.9 m/s.
Some predicted noise spectra for this period are included as Figs. 11-14. One can
see in the noise prediction at 0300 a peak forming at 0.6 Hz with a level of 121 dB.
In subsequent predictions, this peak moves lower in frequency, to 0.45 Hz at 0600,
0.38 Hz at 0900 and finally 0.30 Hz at 1200. The peak level also increases from
121 dB to 125 dB, 130 dB, and finally 133 dB at 1200. It is interesting to note
the wave height power at the peak for this period varies from -13 dB to 12 dB, a
range of 25 dB, while the value of the spreading integral at the peak varies from
-18 dB to -25 dB, for a range of -7 dB. This clearly shows the mitigating effect
of the spreading integral in limiting the noise power at the peak under moderate
conditions.
It is also interesting to consider the predictions in the case of severe weather
conditions. The highest significant wave height recorded for which ECONOMEX
data is available was 5.9 meters at Discus E in the late afternoon of March 4.
Again the wind direction was relatively steady. The meteorological data for this
period is shown in Fig. 32, and the noise predictions for 0400 to 1600 on that
day are seen as Figs.15-21. The peak noise level prediction for this time is 155
dB, with a wave height input of 35 dB and a spreading integral value of -21 dB.
Investigation of our MEM estimates of I,, shows that it reaches a minimum of
about -25 dB at the peak frequency under conditions of moderate wave height (- 3
45
meters), with no further decrease with increasing wave height above that level.
This means our estimated directional distribution is not becoming increasingly
narrow at wave heights above - 3m. This is in disagreement with the observed
behavior of the directional spectra of wave height at high sea state [261. We
might, therefore, expect our predictions to overestimate the noise at high sea
states. The increase in predicted noise level at wave heights above this threshold
will be directly proportional to the increase in the wave height power squared.
At frequencies above the peak, the variation in wave height power with wave
height is much less than that at the peak. One can see that the variation of the
average wave height power on January 27 from 0300 to 1200 in the 0.5 Hz to
0.68 Hz was only from - -20 dB to - -15 dB. This is typical of most of the data
analyzed in this frequency range. Even under the extreme conditions of March 4
the wave height power in this frequency range does not increase much above this
level. Similarly the spreading input varies little in this range of frequencies for a
steady wind direction, varying from - -5 dB to - 0 dB. We would therefore predict
very little variation in the noise level in this frequency range for an increasing sea
state.
6.3 Variation of spectral level with changing wind
direction
One of the more interesting studies we can make involves examining the varia-
tion of noise level under conditions of constant wind speed but changing wind
direction. A theory which proposes that wind turbulence is the direct cause of
the acoustic noise would predict very little variation in noise levels under these
conditions. Thus the predictions we make here may be useful in judging the ac-
tual contribution from the different mechanisms. Under our theory, we intuitively
expect the noise to increase from the increased spread in the directional spectrum
46
as the new wave field is developed, but we also realize the original wave field is
diminishing, due to the loss of wind forcing and the combined effects of dissipation
and non-linear inreractionb with -ie newly developing wave field.
We can see these combined effects in the data from Discus E in the early hours
of February 23, 1991. As we can see in Fig. 33 the wind direction veers sharply
by about 60 degrees at 0200 while the wind speed stays relatively constant at 8
to 11 m/s. The response in the predicted noise spectra is shown in Figs. 22-26.
One can see the noise prediction at the peak is fairly constant at about 135 dB
from 0200 through 0400, then begins to rise until it reaches 140 dB at 0600. The
wave height power input during this period actually drops from 15 dB to 8 dB
at 0400, and it rises back to about 15 dB at 0600. The spreading input at the
peak increases from about -23 dB at 0200 to -17 dB at 0400, and then remains
at about this value through 0600. Thus the increase in predicted noise is due to
the increased spread in the directional spectrum, not an increase in wave height.
Another effect of the wind shift on the predicted acoustic spectrum is that the
peak tends to broaden. This is seen most clearly at 0400 in Fig. 24, when the
peak in the developing wave field and the peak in the pre-existing wave field are
both of similar magnitudes but different frequencies. This behavior is typical of
the wind shifts analyzed.
6.4 Variation of spectral level with receiver depth
The variation in predicted spectral levels with receiver depth can be attributed
to three factors. First, for a receiver in very shallow water, the gravity wave
dispersion relationship will begin to depart from Eq. (4.4) and the bottom will
begin to have an effect on the wave height spectrum. For our receivers at 2500 m
and 450 m, this is not the case. The two remaining factors, the coupling factor
differences and the bottom gain differences, will cause variation in our expected
47
noise levels at these two depths.
Referring to Fig. 5, we can see that the difference in the coupling factor gain
between the two locations varies from about 15 dB at 0.06 hz to about 7 dB at 0.68
Hz, with the shallow site having the higher value. The bottom gain is again more
complicated, with the shallow bottom gain being higher at frequencies less than
0.2 Hz and greater than 0.5 Hz, and the deep bottom gain being higher between
about 0.2 Hz and 0.4 Hz. The combined effects are visible in Fig. 9, where we can
see the differences in the energetic part of the spectrum are quite minimal. Given
the same wave height directional spectrum input, we expect the deep case to yield
higher noise levels of about 6 dB at 0.25 Hz, and we expect the shallow case to
yield higher noise levels of about 5 dB at 0.68 Hz. Due to the limited amount of
data analyzed and the variance of the estimated spectra, it is difficult to see this
variation in the predicted spectra between the two depths. We will therefore not
try to judge the success of the predictions in this area.
48
Chapter 7
Experimental Noise
Measurements
7.1 Experimental description
ECONOMEX (Environmentally Controlled Oceanfloor Noise Monitoring Experi-
ment) [101 was designed to provide a long-term, high quality seismo-acoustic noise
data set which could be coupled to the surface wave and meteorological data of
the SWADE experiment. The instrumentation consisted of six Office of Naval
Research (ONR) ocean bottom seismometers (OBS's) and two, one vertical and
one horizontal, 75 meter six element hydrophone arrays. The instruments were off
the Virginia coast in January 1991, recovered in February 1991 for maintenance
, and redeployed from February through early April 1991. Precise instrument
locations and deployment dates are listed in table 7.1.
The ONR OBS instruments deployed consisted of a three-component geophone
for measuring ground motion in the 0.07 to 80 Hz range, a Cox-Webb differential
pressure gauge (DPG) for measuring long period pressure signals in the water
column, and in the original deployment, an OAS hydrophone [341. In the later
deployment, these hydrophones were removed to improve instrument reliability.
49
O Instrument I Lat. (N) Lon. (W) Depth Deployment dates
Vert. array 370 24.7' 730 26.8' 2573m Jan 25-Feb 6; Feb 22-Apr 5Hor. array 370 24.7' 730 26.8' 2573m Jan 25-Feb 6; Feb 22-Apr 5
OBS 56 370 24.7' 730 26.8' 2548m Jan 25-Feb 6; Feb 22-Apr 5OBS 58 37' 26.4' 73- 31.4' 241;m Jan 24-Feb 7; Feb 22-Apr 5
OBS 61 370 23.8' 730 24.4' 2600m Jan 25-Feb 6; Feb 21-Apr 4
OBS 62 370 33.2' 740 14.1' 769m Jan 11-Feb 6; Feb 22-Apr 5OBS 63 370 Z4.1' 740 16.5' 443m Jan 10-Feb 6; Feb 22-Apr 5OBS 51 370 35.9' 740 21.3' 95m Jan 10-Feb 6; Feb 22-Apr 5
Table 7.1: ECONOMEX instrument summary. Positions and depths listed are forthe second leg of the experiment; those for the first leg differ mly slightly. Alsonote OBS frames 61 and 62 exchanged positions between the first and second legs,although the instruments on them were exchanged also such that the instrumentsremained deployed in the same locations.
The sensors were connected via pi .-amplifiers to an acquisition package consisting
of a pre-whitening and anti-aliasing filter, a gain-ranging amplifier to improve
dynamic range, and an analog to digital converter. The combined filter response
is shown in Fig. 34. The acquisition package fed a recording package consisting of a
RAM buffer and an optical disc recording system capable of storing 400 megabytes
of data. The typical OBS's were programmed for continuous 8 Hz recording, with
the anti-aliasing filter set to 2 Hz; however OBS 56 was set to record at 128 Hz
with its anti-aliasing filter set to 40 Hz.
The 75 meter horizontal and vertical arrays each consisted of six OAS hy-
drophones at 15 meter separation. The hydrophone signals were preamplified by
a low-noise, wide-range preamplifier and sent to acquisition and recording pack-
ages identical to those of the OBS's, with 128 Hz sampling and the anti-aliasing
filter set to 40 Hz. In the second deployment the bottom three hydrophones of
the vertical array were not included due to a cable malfunction. The array cable
jacket included loose ended fiber strands to reduce strumming noise.
50
7.2 Data selection and processing
Following instrument recovery, the ECONOMEX data were transcribed from the
optical disc to magnetic tape. While the data has not yet been transcribed from
the binary machine format to a standard format for further dissemination, it
is possible to read the binary format and produce ASCII files for limited time
periods. The present work has concentrated on using the differential pressure
gauge (DPG) data at the 8 Hz sampling rate to minimize the data processing
involved while still adequately sampling the frequency band of interest. The DPG
data were used instead of the geophone data because of current uncertainties in
the geophone response. Since the model developed is only valid for receivers at
depths greater than 400 meters, it was decided to analyze selected data from one
deep DPG (OBS 58 a, 241-7 m) and the 450 m DPG (OBS 63). This allowed the
maximum depth variation comparison given the instrument deployment depths.
Estimated spectra were generated by removing the mean and any linear trend!
from 64 second segments of the time series, and then averaging 512 poin. fast
Fourier transforms of 34 minute sections of data using a Hanning window. The
response of the pre-whitening and anti-aliasing filter was then removed. The
bandwidth of 64 seconds results in a frequency resolution of 0.0156 Hz, which
is consistent with the spectral resolution of our predictions, which is 0.02 Hz.
An example of a full spectral range observation in shown in Fig. 35. Since the
predictions are limited to a 0.06 to 0.68 Hz band, further observed spectra shown
in this work are limited to the same band for clarity. For the most part, data were
analyzed which corresponded to the same time periods for which predictions were
made in Chap. 6.
51
7.3 Observed results and comparison with pre-
dictions
7.3.1 Spectral shape and overall spectral noise levels
In general, there is good overall agreement between the predicted spectral levels
at most frequencies in the band of interest. Fig. 36 shows an example of one such
case at the 2500 meter site, and Fig. 37 shows similar results at the 450 meter site.
While the levels at a given frequency may differ between predicted and observed
by up to 5 dB, there is an overall correspondence between the two. It is interesting
to note in many of the comparisons between observed and predicted spectra that
small peaks exist in the observed levels which are present in the predictions at
the same frequenies but with differnt magnitudes. These two figures represent
examples of the best agreement between predicted and observed spectra.
More typical of the level of agreement are Figs. 38-43, where we can see close
agreement at frequencies around the spectral peak, but differences away from the
peak of up to 7 dB in the deep case, and up to 17 dB in the shallow case. Here
the overall shape is correctly predicted, but the peak is broader or narrower in
the observed spectra, giving rise to large differences in the high slope region. In
the predictions from the shallow site, there is a tendency to predict levels that are
too high in the band 0.1 Hz to 0.2 Hz. Since this band corresponds to the peak in
the bottom response in the shallow case, errors in the bottom model may account
for this difference.
7.3.2 Variation with wave height
The observations show an increase in noise level with wave height, with good
agreement between observations and predictions at moderate (-.1-3 meters) wave
heights, as seen in Figs. 39-43. At very low predicted noise levels, which corre-
52
spond to times of low wave height, there is a disparity between predictions and
observations. An example of this is the developing wave field of the early hours
of January 27 at Discus E. As one can see in Figs. 44- 46, the agreement is good
at frequencies corresponding to the peak in the predictions as the wave field de-
velops, but the low levels predicted away from the peak are not confirmed by
observation. By 1200 the wave field is developed, and Fig. 39 shows the good
agreement between the prediction and observation at this time. A possible cause
of the error in the predictions at low wave heights is the assumption of spatial ho-
mogeneity of the source wave field. Under very low local wave height conditions,
it is possible for a much stronger w~ve field at some distance to dominate the noise
field, thus making the predictions made from the local wave field very much in
error. Another possible cause of the differences under low wave height conditions
is the existence of another source mechanism generating acoustic energy, whose
noise is normally dominated by that caused by orbital motion. Under low source
strength conditions for the orbital motion noise, this assumed source may now
dominate, giving rise to the errors noted above. The predictions in general are in
reasonably close agreement when measured significant wave height is above - 1
meter. For the period of the ECONOMEX data, roughly 77 percent of the wave
height measurements are above this threshold.
We can see from the data of March 4, as seen in Fig. 47-50, the predictions again
begin to deviate at very high wave height conditions which correspond to strong
winds at relatively constant direction, with the predictions being higher than the
observations. The disagreement at frequencies corresponding to the peak is up to
10 dB under these conditions. There is, however, the same general trend in the
observed noise data as exists in the predictions, that of higher levels at higher
wave heights and wind speeds. This would tend to indicate the wave directional
spectral estimate provided by the MEM technique is overestimating the spread at
these high wave heights. The empirical models, which are based on strong, steady
53
winds, predict less spreading under these conditions than do the MEM estimates.
Thus, under these conditions, the empirical model estimate for the spreading may
be more accurate. The observations match the predictions fairly well in the region
of frequencies above the peak under high wave height conditions.
7.3.3 Variation with changes in wind direction
The predictions agree quite well with the observed data under conditions of chang-
ing wind direction. We can again consider the wind shift of February 23 at 0200,
depicted in Fig. 33, as typical. The observed and predicted noise levels for sub-
sequent times are shown in Figs. 51- 55. The observed noise spectrum changes
with time roughly as the predicted spectrum does. Of particular note is the broad
peak in the observed spectrum at 0400, and the higher levels seen at the peak
from 0500-0700.
It is also interesting to note the predictions and observations during a time
of highly variable conditions such as those of the afternoon of January 27, again
depicted in Fig. 31. The observations and predictions are seen in Figs. 36,56,57.
Again we see relatively close agreement between predictions and observations,
with the increased spreading adding to the noise as the wave height diminishes to
keep the overall noise level fairly constant.
54
Chapter 8
Conclusions and
Recommendations for Future
Research
8.1 Conclusions
The most important conclusion one can draw from this work is the apparent im-
portance of the orbital motion contribution to the total noise level in the frequency
band 0.1 to 0.7 Hz. The close correspondence between the predicted and observed
spectra under a wide range of conditions is strong evidence that the true noise
generation mechanisms in this band are dominated by the interaction of opposing
surface gravity waves. The fact that the predictions hold under the conditions of
changing wind direction but constant wind speed would tend to negate the impor-
tance of the direct input of the wind turbulence on the sea surface as an important
sound generation mechanism under most conditions. There is a possibility that
some other source mechanism or mechanisms contribute significantly to the noise
spectrum in this band under conditions of low wave height.
The second conclusion one may draw from this work is the importance of the
55
measured directional spectrum in determining the overall noise level. Any model
based on empirical relationships using wind speed as their input would have to also
include the growth and decay of the wave field based on changing wind direction.
The models which predict directional wave spectra from a knowledge of wind speed
alone would be doomed to failure in the general case due to their assumption of
a fully developed wave field and the changing nature of the true wave field.
Another important point brought out by this work is the importance of the
propagation mechanisms in determining the overall levels and shape of the acous-
tic noise spectrum in this frequency band, which is consistant with the work
of Schmidt and Kuperman 123). It is imperative that one take into account the
propagation if one wishes to compare source levels between two different locations.
Otherwise differences in the bottom contribution could cloud important correla-
tions or lead to incorrect conclusions. A key element in research of this type is
the geoacoustic bottom model, and the availability of measured wave speeds deep
into the bottom in the present work was extremely fortunate.
8.2 Recommendations for future research
As the predictions of acoustic noise depend so critically on the angular spread of
the wave energy, a fruitful line of investigation would be to obtain directional wave
height spectra of greater angular resolution in future experiments. It is unfortu-
nate that the Spar buoy, the sensor with the greatest directional capability in the
SWADE project, was lost prior to the ECONOMEX deployments. The increased
directional resolution could have been used not only in estimating spectra at the
location of the buoy, but also could have helped in determining the error in the
estimate of the directional spectra made when we use the MEM technique at other
locations. In lieu of higher resolution directional wave spectra, an attempt could
be made to use some of the other SWADE data, such as directional spectral es-
56
timates made by shipborne arrays or radar backscatter, to improve the estimates
from the pitch and roll buoys.
Another investigation which should provide interesting results would be the
correlation of large amounts of the ECONOMEX data with the various SWADE
parameters such as wind speed and wave height, and perhaps to automate the gen-
eration of acoustic predictions from the SWADE directional spectra. The present
research only scratched the surface of the data available from this long term ex-
periment. It would be useful to find the amount of long term agreement, and even
more interesting to find other periods of disagreement between the predictions
made with the model developed herein and ECONOMEX observations.
The final recommendation for research in this area would be the investigation
of the range dependent aspects of the problem. There is range dependence in
the both the source mechanism and the propagation mechanisms, which perhaps
gives rise to some of the disagreement between our predictions and observations.
The shallow site, in particular, would benefit from a consideration of its range
dependent bathymetry. Buckingham [331 has found the noise in a wedged-shaped
ocean with pressure-release boundaries to closely apprqximate the noise field in
the range independent case, but further work is needed to extend his work to a
more general bottom. As well, the investigation of the spatial variation of the
wave height spectrum should prove feasible once the entire SWADE project data
is collected and correlated. This could then be used to more accurately predict
the noise at the ECONOMEX sites.
57
Bibliography
[I] M. S. Longuet-Higgins, "A theory of the origin of microseisms," Philos. Trans.R. Soc. London Ser. A 243, 1-35 (1950).
12] L. M. Brekhovskikh, "Underwater sound waves generated by surface wavesin the ocean," izv. Atmos. Ocean Phys. 2, 582-587 (1966).
[31 A. C. Kibblewhite and C. Y. Wu, "The generation of infrasonic ambient noisein the ocean by nonlinear interactions of ocean surface waves.' J. Acoust. Soc.Am. 85, 1935-1945 (1989).
[4) D. H. Cato, "Sound generation in the vicinity of the sea surface: sourcemechanisms and the coupling to the received sound field," J. Acoust. Soc.Am. 89, 1076-1095 (1991).
[5] Y. P. Guo, "Waves induced by sources near the ocean surface," J. Fluid Mech.181, 293-310 (1987).
[61 R. H. Nichols, 'Infrasonic ambient ocean noise measurements: Eleuthera,"J. Acoust. Soc. Am. 69, 974-981 (1981).
[7] T. E. Tapley and R. D. Worley, "Infrasonic ambient noise measurements indeep Atlantic water," J. Acoust. Soc. Am. 75, 621-622 (1984).
18] I. G. Adair, J. A. Orcutt, and T. H. Jordan "Low-frequency noise observa-tions in the deep ocean," J. Acoust. Soc. Am. 80, 633-645 (1986).
[91 G. H. Sutton and N. Barstow, "Ocean-bottom ultralow-frequency (ULF)seismo-acoustic ambient noise: 0.002 to 0.4 Hz," J. Acoust. Soc. Am. 87,2005-2011 (1990).
1101 G. M. Purdy and G. V. Frisk, "A long term experiment to monitor lowfrequency noise across the east coast of the U.S.," Woods Hole OceanographicInstitution, Proposal No. 6000.32R, Woods Hole, MA (Nov. 29, 1989).
[111 J. A. Orcutt, "Sources of ambient microseismic oceanic noise (SAMSON),"Scripps Institution of Oceanography, USDC Proposal No. 89-1471, La Jolla,CA (May 17, 1989).
58
[12] D. H. Cato, "Theoretical and measured underwater noise from surface waveorbital motion," J. Acoust. Soc. Am. 89, 1096-1112 (1991).
[13] H. Schmidt, SAFARI. Seismo-Acoustic Fast Field Algorithm for Range Inde-pendent Environments. User's Guide SACLANT ASW Research Center, LaSpezia, Italy SR 113 (1987).
[14] H. Schmidt and F. B. Jensen, " A full wave solution for propagation inmultilayered viscoelastic media with application to Gaussian beam reflectionat fluid-solid interfaces," J. Acoust. Soc. 1m. 77, 813-825 (1985).
[15] R. E. Sheridan, D. L. Musser, L. Glover III, M. Talwani, J. Ewing, S. Hol-brook, G. M. Purdy, R. Hawman, and S. Smithson, "EDGE deep seismicreflection study of the U.S. mid-Atlantic continental margin," Am. Geophys.Union 72, EOS, Transactions, Spring Meeting, 273-274 (1991).
[16] M. J. Lighthill, "On sound generated aerodynamically: I. General theory,"Proc. of the R. Soc. A211, 564-578 (1952).
[17] Lord Rayleigh, Theory of Sound (Dover Publications, New York, second edi-tion, 1945 reissue) (1877).
[18] P. E. Doak, "Analysis of internally generated sound in continuous materials:2. A critical review of the conceptual adequacy and physical scope of existingtheories of aerodynamic noise, with special reference to supersonic jet noise,"J. Sound Vib. 25, 263-335. (1972).
[19] J. A. Stratton, Electromagnetic Theory, McGraw-Hill, New York (1941).
[20] N. Curie, "The influence of solid bouL zries upon aerodynamic sound," Proc.R. Soc. of London Series A 231, 505-514 (1955).
[211 G. K. Bachelor, An Introduction to Fluid Dynamics, Cambridge UniversityPress, Cambridge (1970).
[22] 0. M. Phillips The Dynamics of the Upper Ocean, Cambridge UniversityPress, London, (1966).
[23] H. Schmidt and W. A. Kuperman, " Estimation of surface noise source levelfrom low-frequency seismoacoustic ambient noise measurements," J. Acoust.Soc. Am. 84, 2153-2162 (1988).
[24] R. A. Weller, M. A. Donelan, M. G. Briscoe, and N. E. Huang, "Riding thecrest: a tale of two experiments," Bull. Am. Meteor. Soc. 72,163-183 (1991).
59
[25] M. S. Longuet-Higgins, D. E. Cartwright, and N. D. Smith, "Observations ofthe directional spectrum of sea waves using the motions of a floating buoy,"Ocean Wave Spectra Prentice-Hall, Englewood Cliffs, New Jersey (1963).
[26] M. A. Donelan, J. Hamilton, and W. H. Hui, "Directional spectra of wind-generated waves," Trans. R. Soc. London Ser. A 315, 509-562 (1985).
[27] A. Lygre and H. E. Krogstad, "Maximum entropy estimation of the direc-
tional distribution in ocean wave spectra," J. Phys. Oceanogr. 16, 2052-2060(1986).
[28] J. P. Burg, "Maximum entropy spectral analysis" Ph.D. dissertation StanfordUniversity (1976).
[29] E. L. Hamilton, "Geoacoustic modeling of the sea floor," J. Acoust. Soc. Am.
68, 1313-1340 (1980).
[30] S. Holbrook, Private communication, (1991).
[31] J. Ewing, Private communication, (1991).
1321 H. Mitsuyasu, F. Tsai, T. Suhara, S. Mizuno, M. Ohkuso, T. Honda, andK. Rikiisi, "Observations of the directional spectrum of ocean waves using acloverleaf buoy," J. Phys. Oceanog. 5, 750-760 (1975).
[33] M. J. Buckingham, "A theoretical model of surface-generated noise in awedge-shaped ocean with pressure-release boundaries," J. Acoust. Soc. Am.78, 143-148 (1985).
[34] G. M. Purdy, L. Dorman, A. Schultz, and S. C. Solomon, "An ocean bottomseismometer for the Office of Naval Research," in ULF/VLF (0.001 to 50 Hz)Seismo-Acoustic Noise in the Ocean, Proceedings of a workshop at the Irwti-tute for Geophysics, University of Texas, Austin, November 29 to December
1, 1988, edited by G. H. Sutton (1990).
[35] R. T. Lacoss, "Data adaptive spectral analysis methods," Geophysics 86,661-675 (1971).
60
ECONOMEX and SWADE instrument locations39
Discus N.*A
38
Virginia Discus C and 3 OBS's
00
DiscusE, 3 OBS's, and arrays
3777 76 75 74 73
Longitude
Figure 1: Approximate locations of the ECONOMEX and relevant SWADE instru-ments. "*' denotes pitch and roll buoy location, "x' denotes location ofone ONR OBS and two hydrophone arrays, and "o' denotes the locationof one ONR OBS.
61
OBOOS B
OHSorizoltralyra(75m)
-60km
Figure 2: Schematic arrangement of ECONOMEX and SWADE deployments.
62
MEM estimate MLM estimate0.8 0.8
- Tre spectrm
0.7 0.7---- Estimated spectrum
0.6- 0.6
0.5 (a) 0.5 (b)o 0Vt
.0.40.4- 0.4-
0.2 0.2
0.1- 0.1!
0 01-100 0 100 -1o 0 100
Angle (degrees) Angle (degrees)
LCS estimate Empirical estimate0.8 0.8
0.7 - 0.7
0.6- 0.6
0.5- (c) 0.5 (d)o 0
0.23 0.32
0.1 - 0.1
0 1 0
-100 0 100 -100 0 100
Angle (degrees) Angle (degrees)
Figure 3: Estimates of the directional spectrum of G(-/) = N(coss (-1/2)+cos'°('y/2+ir/4)), where -y is the azimuthal angle, and N is chosen to normalize thespectrum. The MEM estimate was made using the Lygre-Krogstad al-gorithm mentioned in the text. The MLM estimate was made using analgorithm by Lacoss (351. The LCS estimate refers to the weighted aver-age of the first five Fourier coefficients suggested by Longuet-Higgins etal. [25] The empirical estimate was made by estimating the parameters from the first five Fourier coefficients and using the empirical formulaG(-y) = Ncos"(-y/2).
63
Directional spectral estimates for Discus E at 0.16 Hz, 1127/91 1200
1.4 - MEM estimate
------ MLM estimate
1.2 .......... L C S estim ate--....... Empirical estimate
0.8o 5
0.6 ,.,
0.4 .... ,..
0.2
-150 -100 -50 0
Angle (degrees)
Figure 4: Estimated spectra derived from the 0.16 Hs data bin from the Discus Ebuoy on January 27, 1991 at 1200 hours. The estimates were made usingthe methods discussed in the caption to Fig. 3.
64
Coupling factor integrals; 2500 mn and 450 m receivers
-55 - Shallow vertical .............. - - - . . . . - .
............... Shallow horizoal
-60 - ...
U -75-
-80- Deep horizontal--------------- Deep vertical
-850 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Frequency (Hz)
Figure 5: Plots of 1Ologfk(H 1 Hj + H2H)kdk and 10logfO4 H3,H-kdk for re-ceiver depths of 450 meters and 2500 meters. ko was taken as 5w/c, andan effective radius of 100 kilometers was used.
65
Wave speed profile - deep site
0
1000-
2000 (a)
3000
4000 Cp
S 5000-
000-
7000-
8000s
9000-C
10000,0 1000 2000 3000 4000 5000 6000 7000
Wave Speed (m/s)
Wave speed profile - shallow site
0
1000
2000 (b)
3000-
4000 C Cp
• 5000-
7000
8000-
9000
100000 1000 2000 3000 4000 5000 6000 7000
Wave Speed (mi/s)
Figure 6: Profiles of compressional and shear wave speeds, Cp and Cs, used in the en-
vironmental model. Compressional wave speeds are based on unpublished
data from the EDGE deep seismic reflection survey, and the shear wave
speeds were derived from the compressional wave speeds, as described inthe text. Figure 6a is the deep site and Fig. 6b is the shallow site.
66
".torn Gain241
22.. Shallow horizontal- - -- Shallow vertical: " "Deep horizontal
20.... . Deep vertical
18 *
16 *
14"
8 - I
12 *., -,
6 . ........4i
1 0.1 0:2 0.3 04 0.5 0.6 0.7
Figure 7: Plots of 7~from data generated by SAFARI for the assumed bottommodel at 450 mx and 2500 m receiver depths for m = 1 and m = 2.
67
0. 1
m~ 0. ia-
37.0- 41.
170- 21.0
0.7BEIDW 1.00. 0.1 0.2 0.3 0.4 0.5 0.8 0 .7
Slowness (s/kin)Deep site integrands
0.1
0O.3ABOVEL 29.0
00. 21.0 -25.017.0 - 21.013.0 - 17.0
0.5 B g.0 - 13.0- 5.0 - 9.0r 1.0 - 5.0
rj -3.0 - L.0
7 -7.0 - -3.0.11 1]-11.0 - -7.0
0.7 m BELOW -11.0
0. 1.0 2.0 3.0 4.0 5.0Slowness (s/kin)
Shallow site integrands
Figure 8: Contours of the integrands of Eq. (4.41), the depth-dependent Green'sfunctions g(k, z, z'), versus horizontal slowness 1/c = k/u and frequencyfor a) the deep site (2500 m) and b) the shallow site (450 in).
68
Overall transfer function 10 log B(f)
160
155-
150-
145-
S140-
S135 Deep site
130- ------- Shallow site
125-
1200 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Frequency (Hz)
Figure 9: Plots of 10 log B(f ) for the deep and shallow sites.
69
Spreading integral versus frequency using Donelan's empirical model
-20
-25
-30
~-35
-50
-55
-6010.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Frequency (f/fO)
Figure 10: Plot of 10 log I.,, versus normalised frequency f/fo using Donelan's em-pirical model for the directional wave spectrum [261 where fo is doublethe frequency at the peak in the wave height spectrum.
70
125 2500 m, 1/27/91, 0300 0.25 Discus E
1-120 (a) 0.2 (b)
: 115 0.15G) 0
110 " 0.1z
105 - 0.05-
100 00.2 0.4 0.6 0.8 0.1 0.2 0.3 0.4
Acoustic Frequency (Hz) Wave Frequency (Hz)
-10 Wave height acoustic input -5_Discus E
-20 c) -(d)o -10
-30• -15-
S-40o
€-50 ' -20'C4 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8
Acoustic Frequency (Hz) Acoustic Frequency (Hz)
Figure 11: Predicted noise level and inputs for a 2500 meter receiver on 1/27/91 at0300. a) Noise spectral level 10logP(f) in dB re pPa2/Hs. b) Waveheight power spectrum fl(o,/) in m2/Hz. c) Wave height acoustic input20 log fl(f/2) in dB re m2/Hs. d) Spreading integral level 10 log I.. (f)in dB re Hz - .
71
130 2500m 1/27/91,0600 0.6 Discus E
1-125 (a) (b)
120- 0.4-
0M~115 -0.0 0 .2 - ^
110
105 00.2 0.4 0.6 0.8 0.1 0.2 0.3 0.4
Acoustic Frequency (Hz) Wave Frequency (Hz)
0 Wave height acoustic input Discus E
B -10 (c) - -10 (d)0
X -20 - -15oto
-30 - 1 -20o
-0 '-25'0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8
Acoustic Frequency (Hz) Acoustic Frequency (Hz)
Figure 12: Predicted noise level and inputs for a 2500 m receiver on 1/27/91 at 0600.a) Noise spectral level 10 log P(f) in dB re pPa2/Hs. b) Wave height powerspectrum fl(a/21r) in m 2 /Hs. c) Wave height acoustic input 20 log 0(1/2)in dB re m 2/Hs. d) Spreading integral level 10 log I.,, (f) in dB re Hs - 1 .
72
140 2500 n, 1/27/91,,0900 2.5 Discus E
130(a) 2 (b)
120 1.5
110
~100 0.5-
90 00.2 0.4 0.6 0.8 0.1 0.2 0.3 0.4
Acoustic Frequency (Hz) Wave Frequency (Hz)10 Wave height acoustic input -5 Discus E
(c) (d)-10 -15~-10
0-20 -20-
-30 - -25
4-40 -300.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8
Acoustic Frequency (Hz) Acoustic Frequency (Hz)
Figure 13: Predicted noise level and inputs for a 2500 m receiver on 1/27/91 at 0900.a) Noise spectral level 10 log P(f) in dB re pPa2 /Hs. b) Wave height powerspectrum fl(o/2wr) in m 2/Hs. c) Wave height acoustic input 20 log fl(f/2)in dB re m2/Hs. d) Spreading integral level 1Olog I., (f) in dB re Hs - .
73
10 2500 mn, 1/27/91, 1200 5Discus E
130 (a) 4- (b)
4)0
2-z110 1
100 00.2 0.4 0.6 0.8 0.1 0.2 0.3 0.4
Acoustic Frequency (Hz) Wave Frequency (Hz)
20 Wave height acoustic input Discus E10 -5(d
15 l-c F _120-dCU
~-20 - -25-
~-30 -30'0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8
Acoustic Frequency (Hz) Acoustic Frequency (Hz)
Figure 14: Predicted noise level and inputs for a 2500 m receiver on 1/27/91 at 1200.a) Noise spectral level 10 log P(f) in dB re #Pa2/Hs. b) Wave height powerspectrum 0l(ao/2) in M2 /HS. c) Wave height acoustic input 20 log 0 (f/2)in dB rem m2 /Hs. d) Spreading integral level 10 log I.,,(f ) in dB re Hs1
74
2500 m,3/491, 0400 Discus E155 25
15-(a) 20- (b)~~15-
,0135-• 2 10°
125-S 5-
115 :R: 00 0.2 0.4 0.6 0.8 0 0.1 0.2 0.3 0.4
Acoustic Frequency (Hz) Wave Frequency (Hz)
Wave height acoustic input Discus E~30 ------- -5
120 F8(c) .~-10- (d)
1-15
-0-20
-20 -2510 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8
Acoustic Frequency (Hz) Acoustic Frequency (Hz)
Figure 15: Predicted noise level and inputs for a 2500 m receiver on 3/04/91 at 0400.a) Noise spectral level 10 log P(f) in dB re IPa 2 /Hs. b) Wave height powerspectrum fl(a/21r) in m2 /Hs. c) Wave height acoustic input 20 log (l(f/2)in dB re m2 /Hs. d) Spreading integral level 10 log I.,, (f) in dB re Hs 1 .
75
15 2500 m, 3/049, 0600 30Discus E
-145 -(a) (b)'20-
135-1
M~125'IV 10-
~115-
105 0 L0 0.2 0.4 0.6 0.8 0 0.1 0.2 0.3 0.4
Acoustic Frequency (Hz) Wave Frequency (Hz)
Wave height acoustic input - Discus ET--
S20- (c) .~-10- (d)
0- ~-15-
~-20 - -20-
N400 0.2 0.4 0.6 0.8 -50 0.2 0.4 0.6 0.8Acoustic Frequency (Hz) Acoustic Frequency (Hz)
Figure 16: Predicted noise level and inputs for a 2500 mn receiver on 3/04/91 at 0600.a) Noise spectral level 10 log P(f) in dB re #Pa2/Hs. b) Wave height powerspectrum fl(ao/2r) in M2/Hs. c) Wave height acoustic input 20 log 11(f/2)mn dB re wu2 /Hs. d) Spreading integral level 10 log I.,, (f) in dB re Hs 1
76
155 2500m 304 2 1 0800 40Discus E
u4 143 (a) 30- (b)
0 135- 20-
125-~ 10-
110 02 0.4 0.6 0.8 0 0.1 0 .2 0. 0.4
Wave heighit acoustic input - Discus E
(C) -10-(d)
~-15-
0- ~-20-
~-20 -25'0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8
Acoustic Frequency (Hz) Acoustic Frequency (Hz)
Figure 17: Predicted noise level and inputs for a 2500 m receiver on 3/04/91 at 0800.a) Noise spectral level 10 log P(f ) in dB re MuPa 2/HI. b) Wave height powerspectrum fl(au/2ir) in m2 /Hs. c) Wave height acoustic input 20 log f)(f/2)in dB re m2 /Hs. d) Spreading integral level 10 log I.,, 3 (f) in dB re Hs 1
77
Predctedspqqp 3[4/91000Wave hei ht Discus E
145-N40-
S135-1r
125- 20
115 00 0.2 0.4 0.6 0.8 0 0.1 0.2 0.3 0.4
Acoustic Frequency (Hz) Wave Frequency (Hz)
Wave height power in dB -5Spreading integral.40-
-10-20-
~-15
0 - -20 -
-20 -250 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8
Acoustic Frequency (Hz) Acoustic Frequency (Hz)
Figure 18: Predicted noise level and inputs for a 2500 m receiver on 3/04/91 at 1000.a) Noise spectral level 10 log P(f) in dB re pPa2 /Hs. b) Wave height powerspectrum f)(o/2ir) in M2 /11s. c) Wave height acoustic input 20 log 11(f /2)in dB re m2 /Hs. d) Spreading integral level 10 log I.,,i (f ) in dB re Hs-'.
78
155 2500 m, 34/91, 1200 40 Discus E
" 145 (a) 30 (b)
o o-
• 00135- 0
o. 125-t 10-
115 0-0 0.2 0.4 0.6 0.8 0 0.1 0.2 0.3 0.4
Acoustic Frequency (Hz) Wave Frequency (Hz)
40 - Wave height acoustic input 5 Discus E
(c) . I -1 (d)S20
~-15-
S-20
C-20 -2510 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8
Acoustic Frequency (Hz) Acoustic Frequency (Hz)
Figure 19: Predicted noise level and inputs for a 2500 m receiver on 3/04/91 at 1200.a) Noise spectral level 10 log P(f) in dB re pPa2/Hs. b) Wave height powerspectrum flo/21r) in m2/Hs. c) Wave height acoustic input 20 log f(1/2)in dB re m2/Hs. d) Spreading integral level 10 log I,, () in dB re Hs 1.
79
155 2500mn, 2M , 14004 Discus E
145(a) ~ 0(b)30-
1.)135- 20-
z 125 -10-
115. 0.0 0.2 0.4 0.6 0.8 0 0.1 0.2 0.3 0.4
Acoustic Frequency (Hz) Wave Frequency (Hz)
Wave height acoustic input Discus E~30 -
20- F9(d)20(c) a lo
0-
.5 -15-
*0
~-20' -2010 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8
Acoustic Frequency (Hz) Acoustic Frequency (Hz)
Figure 20: Predicted noise level and inputs for a 2500 m receiver on 3/04/91 at 1400.a) Noise spectral level 10 log P(f) in dB re psPa2 /Hs. b) Wave height powerspectrum fl(o/2) in nM2 /Hs. c) Wave height acoustic input 20 log f(f(/2)in dB re m2 /Hs. d) Spreading integral level 10 log I.. (f ) in dB re Hs 1
80
155 2500 m,3/49, 1600 40 Discus E
4145- (a) 30 (b)
135 - 20
-- 125 IZ I0-
105 0
0 0.2 0.4 0.6 0.8 0 0.1 0.2 0.3 0.4
Acoustic Frequency (Hz) Wave Frequency (Hz)
Wave height acoustic input Discus E
'--5
(c) -10 (d)~20-
415
0--15
~-20-
(-20 -25-0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8
Acoustic Frequency (Hz) Acoustic Frequency (Hz)
Figure 21: Predicted aoise level and inputs for a 2500 m receiver on 3/04/91 at 1600.a) Noise spectral level 10 log P(f) in dB re 1Pa2/Hs. b) Wave height powerspectrum fO(u/2w) in m2 /Hs. c) Wave height acoustic input 20 log 11(f /2)in dB re m2/Hz. d) Spreading integral level 10 log I.. (f) in dB re Hs-'.
81
130 2500 m, 2/23/91, 0200 8 Discus E130 1120 (b)
o 4V 110 -4-
100
90 , : 0-
0 0.2 0.4 0.6 0.8 0 0.1 0.2 0.3 0.4
Acoustic Frequency (Hz) Wave Frequency (Hz)
Wave height acoustic input -10 Discus E~20 ---- 1
o 10"-(c) (d)o ~-150
-
.. -20-20 -o
(0-30 CIO) -251
0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8
Acoustic Frequency (Hz) Acoustic Frequency (Hz)
Figure 22: Predicted noise level and inputs for a 2500 m receiver on 2/23/91 at 0200.a) Noise spectral level 10 log P(f) in dB re pPa2 /Hs. b) Wave height power
spectrum fl(a./21r) in m 2/Hs. c) Wave height acoustic input 20 log fl(f/2)in dB re m2 /Hs. d) Spreading integral level 10 log Ia, (f) in dB re Hs 1 .
82
135 2500 m,2/3/91, 0300 4 Discus E
(a) (b)125 3-
0115 2
.105 1
95 0.0 0.2 0.4 0.6 0.8 0 0.1 0.2 0.3 0.4
Acoustic Frequency (Hz) Wave Frequency (Hz)
v ght acoustic input Discus E20 Wa e he ousticut_-5, , ,
(c)- -10"0 0-
S-15
M -20 .I -20
oI -
,-40 - -250 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8
Acoustic Frequency (Hz) Acoustic Frequency (Hz)
Figure 23: Predicted noise level and inputs for a 2500 m rcceiver on 2/23/91 at 0300.a) Noise spectral level 10 log P(f) in dB re uPa2/Hs. b) Wave height powerspectrum fl(a/2r) in m 2/Hz. c) Wave height acoustic input 20 log fl(f/2)in dB re m2 /Hs. d) Spreading integral level 10log I.,, (f) in dB re Hs - .
83
135 2500A 223/91, 0400 3 Discus E
0 -(a) (b)°2-
125
.-120z115110 0. :
0.2 0.4 0.6 0.8 0.1 0.2 0.3 0.4
Acoustic Frequency (Hz) Wave Frequency (Hz)10 Wave height acoustic input -5 Discus E
-- -- - -- - - - -
0 (c) I- - (d)
-10 -15
20 -20o
-30 -250.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8
Acoustic Frequency (Hz) Acoustic Frequency (Hz)
Figure 24: Predicted noise level and inputs for a 2500 m receiver on 2/23/91 at 0400.a) Noise spectral level 10 log P(f) in dB re pPa2 /Hs. b) Wave height powerspectrum fl(o/21r) in m 2 /Hs. c) Wave height acoustic input 20 log f0(f/2)in dB re m 2/Hs. d) Spreading integral level 10 log I. (f) in dB re Hz - '.
84
140 2500 m, 2/23/91,0500 5 Discus E
(a) 4 (b)$0'130-
o 30 120 -
2-o.1101
100 ,00 0.2 0.4 0.6 0.8 0 0.1 0.2 0.3 0.4
Acoustic Frequency (Hz) Wave Frequency (Hz)
20 Wave height acoustic input Discus Eo10- -
( 1C) -10 (d)
4 -10-
,-20~-20
'0 -30- -25.0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8Acoustic Frequency (Hz) Acoustic Frequency (Hz)
Figure 25: Predicted noise level and inputs for a 2500 m receiver on 2/23/91 at 0500.a) Noise spectral level 10 log P(f) in dB re MPa 2/H s . b) Wave height power
spectrum fl(o/21) in m2/Hs. c) Wave height acoustic input 20 log fl(f/2)in dB re m2/Hs. d) Spreading integral level 10log Ia,, (f) in dB re Hs-.
85
145 2500m 2/23/91, 0600 8 Discus E
'15 (a) (b).
0125z 115 2-
105 00.2 0.4 0.6 0.8 0.1 0.2 0.3 0.4
Acoustic Frequency (Hz) Wave Frequency (Hz)
20 Wave height acoustic input Discus E
10 (C) (d)g) -lo-
o -10• -15
S-20 -
-30I -200.2 0.4 0.6 0,8 0.2 0.4 0.6 0.8
Acoustic Frequency (Hz) Acoustic Frequency (Hz)
Figure 26: Predicted noise level and inputs for a 2500 m receiver on 2/23/91 at 0600.a) Noise spectral level 10 log P(f) in dB repPa2 /Hs. b) Wave height powerspectrum fl(a/2r) in m2 /Hs. c) Wave height acoustic input 20 log fl(f/2)in dB re m2 /Hs. d) Spreading integral level 10log I.., (f) in dB re Hz - 1.
86
135 450 m, 3/91 1000 4 Discus C
F125- (a) (b)3-
1154) 0 2-
"o 105 -
95-Ce
85 00 0.2 0.4 0.6 0.8 0 0.1 0.2 0.3 0.4
Acoustic frequency (Hz) Wave frequency (Hz)
-20 Wave height acoustic input 0 Discus C
20 0
0-(c) (d)S-10
Cd -20 .R -20
o -250 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8
Acoustic frequency (Hz) Acoustic frequency (Hz)
Figure 27: Predicted noise level and inputs for a 450 m receiver on 2/23/91 at 1000. a)Noise spectral level 10 log P( f) in dB re pPa2/Hs. b) Wave height powerspectrum fl(a/2x) in m2/Hs. c) Wave height acoustic input 20 log fO(f/2)in dB re m2/Hs. d) Spreading integral level 10log I.,, (f) in dB re Hs- 1 .
87
450 m, 2/23/91, 1400 Discus C1406
a (b)120 4
0 4-
04)0 0
0 2S80 -
60, 00 0.2 0.4 0.6 0.8 0 0.1 0.2 0.3 0.4
Acoustic frequency (Hz) Wave frequency (Hz)
Wave height acoustic input Discus C~200
F9--5
0- (c) (d)0CI -to -
-20 10
-4 -20
C4 -60 ' -250 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8
Acoustic frequency (Hz) Acoustic frequency (Hz)
Figure 28: Predicted noise level and inputs for a 450 m receiver on 2/23/91 at 1400. a)Noise spectrai level 10 log P(f) in dB re pPa2 /Hs. b) Wave height powerspectrum fl(o/2r) in m2 /Hs. c) Wave height acoustic input 20 log fl(f/2)in dB re m2 /Hs. d) Spreading integral level 10log I.,, (f) in dB re HI-'.
88
450 mr, 7 1. 1500 Discus C135 8130 (a) (b)
125 -0 4-
M 1200z 2
115 2-
110--_ 00 0.2 0.4 0.6 0.8 0 0.1 0.2 0.3 0.4
Acoustic Frequency (Hz) Wave Frequency (Hz)
20 Wave height acoustic input Discus C
20 10 -5l-(c) lu-(d)
: -15-V -10
-20_- I 20-30 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8
Acoustic Frequency (Hz) Acoustic Frequency (Hz)
Figure 29: Predicted noise level and inputs for a 450 m receiver on 2/27/91 at 1500. a)Noise spectral level 10 log P(f) in dB re uPa2 /Hs. b) Wave height powerspectrum fl(cr/2r) in m2/Hs. c) Wave height acoustic input 20 log fl(f/2)in dB re m2 /Hs. d) Spreading integral level 10log I.,, (f) in dB rt Hs- 1.
89
450 n, "_.7/1, 1800 3Discus C130 3 9
1 -125-( (b)I2-
120-44)0
*115z
110-
105'-- 00 0.2 0.4 0.6 0.8 0 0.1 0.2 0.3 0.4
Acoutic Frequency (Hz) Wave Frequency (Hz)
Wave height acoustic input Discus C~10 -5I
(c) -10- (d)
~-15-0 -20-
-30 - -20-
N 4 -25'0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8
Acoustic Frequency (Hz) Acoustic Frequency (Hz)
Figure 30: Predicted noise level and inputs for a 450 m receiver on 2/27/91 at 1800. a)Noise spectral level 10 log P(f) in dB re psPa2 /Hs. b) Wave h.,ght powerspectrum fl(o/2r) in M2 /Hz. c) Wave height acoustic input 20 log 0l(f/2)in dB rem m2 /Hs. d) Spreading integral level 10 log I.,,(f ) in dB re Its 1
90
Wind vector, 1/2 7i91, Discus E
15
10 (a)
Downward vertical arrow indicates wind from the west
10-
150000 0448 0936 1424 1912 2400
Thne of Day
Wind speed and wave height, 1/27/91, Discus E12 2
10. (b)
8 - ,
6-) so"I
2- ---- Wind speed
Wave height
0C 00000 1200 2400
Tume of Day
Figure 31: Meteorological data as measured at Discus E on 1/27/91. a) Wind vector.The direction of the arrow indicates the direction of the wind, with a
downward arrow indicating a wind from the west. The magnitude of thearrow indicates the wind speed, with the wind speed scale given on thevertical axis. b) Wind speed and wave height.
91
Wind vector, 3/4/91. Discus E
15
10 (a)
Downward vertical arrow indicates wind from the west
5-
0
10-
15
0000 1200 2400
Tune of Day
Wind speed and wave height, 3/4/91, Discus E20 . ... .0
16 (b) 8
.. . .. .. . ,, -
8 --
- - Wind speed
Wave height
0000 1200 2400
Time of Day
Figure 32: Meteorological data as measured at Discus E on 3/04/91. a) Wind vector.The direction of the arrow indicates the direction of the wind, with adownward arrow indicating a wind from the west. The magnitude of thearrow indicates the wind speed, with the wind speed scale given on thevertical axis. b) Wind speed and wave height.
92
Wind vector, 1200 2/22/91 - 1200 2/23/91, Discus E10
(a)
5-Downward vertical arrow indicates wind from the west
I0-'
222 1200 2/230000 2/231200
Tune of Day
Wind speed and wave height, 1200 2/22/91 - 1200 2123/91, Discus E18 . .. . . . . 3
16 Wind speed
14 Wave height (b)
12
0 '
2/221200 2/230000 2/231200
Time of Day
Figure 33: Meteorological data as measured at Discus E on 2/22/91-2/23/91. a)Wind vector. The direction of the arrow indicates the direction of thewind, with a downward arrow indicating a wind from the west. Themagnitude of the arrow indicates the wind speed, with the wind speedscale given on the vertical axis. b) Wind speed and wave height.
93
ONR OBS combined filter response0 I I I I * I I I I1 1 1
-5-
-10-
-40
10210-1 100 101
Frequency (Hz)
Figure 34: Amplitude response of the anti-aliasing and pre-whitening filter used inthe ECONOMEX instruments with an 8 Hs sampling rate. Responseamplitude in dB re 1 Volt.
94
Estimated spectrum OBS 58 DPG 3/4/91 1700
150-
140
130
120
S110
100
90
80
7010-3 10-2 10-1 100 101
Frequency
Figure 35: An example of a full spectral estimate using data from OBS 58 DPG on
3/04/91 at about 1700 hours. This spectrum was generated as described
in the text with the exception that a 2048 point FFT was used versus a
512 point FFT. The spectral level is in dB re pPa2 /Hs.
95
2500 m, 1/27/91, 1800 450 m, 2/23/91, 1400
145 145
140 140
135- 135- -'
130 UM 130 130-
S125 - 125 -
III 0
z120 * 120-
115 115-
110 110-
105 1050 0.2 0.4 0.6 0 0.2 0.4 0.6
Frequency (Hz) Frequency (Hz)
Figure 36: Predicted and observed noise lev- Figure 37: Predicted and observed noise lev-els, 1/27/91, 1800, OBS 58 (2500 els, 2/23/91, 1400, OBS 63 (450m), in dB re pAPa 2 /Hs. Observed m), in dB re ppa2 /Hz. Observedspectrum is solid curve, spectrum is solid curve.
96
2500 m, 2/23/91, 0700 2500 m, 1/27/91, 1200145 145
140 140I'
135- 135/,,130 ; , 130-
4) 40 125 % 0 125
z 120, z 120•
II t
115 *,115'
110 110
105 1 10510 0.2 0.4 0.6 0 0.2 0.4 0.6
Frequency (Hz) Frequency (Hz)
Figure 38: Predicted and observed noise lev- Figure 39: Predicted and observed noise lev-els, 2/23/91, 0700, OBS 58 (2500 els, 1/27/91, 1200, OBS 58 (2500m), in dB re pPa2/Hs. Observed m), in dB re pPa2/Hs. Observedspectrum is solid curve, spectrum is solid curve.
97
2500 m, 3/U4/91, 0000 450 m, 227/91, 18001451 145
140, 140, *
* a* a
135 135* a
S130 M 130
125 a, 125 -
0 0
z 120 z 120 - a
115 -,115-
110 a 110
105 -- 105 '0 0.2 0.4 0.6 0 0.2 0.4 0.6
Frequency (Hz) Frequency (Hz)
Figure 40: Predicted and observed noise lev- Figure 41: Predicted and observed noise lev-els, 3/04/91, 0000, OBS 58 (2500 els, 2/27/91, 1800, OBS 63 (450m), in dB re pPa2 /Hz. Observed m), in dB re pPa2 /H. Observedspectrum is solid curve. spectrum is solid curve.
98
450 m, 2/27/91, 1500 450 m, 2/23/91, 1000
145 145
140- 140
135 135-
c130 -130- t
12 ,2125,12* ,
0 'a
.V
115- 115-
1I /110-
110105-
1050 0.2 0.4 0.6 0 0.2 0.4 0.6
Frequency (Hz) Frequency (Hz)
Figure 42: Predicted and observed noise lev- Figure 43: Predicted and observed noise lev-els, 2/27/91, 1500, OBS 63 (450 els, 2/23/91, 1000, OBS 63 (450m), in dB re sPa2/Hs. Observed m), in dB re pPa2 /H. Observedspectrum is solid curve, spectrum is solid curve.
99
2500 m, 1/27/91, 0300 2500 m, 1/27/91, 0600
145 145
140 140
135 135
' 130 - 130
125 - 125-
z120 z 120,
110 110,.
115 1, -, , a
0 0.2 0.4 0.6 0 0.2 0.4 0.6
Frequency (Hz) Frequency (Hz)
Figure 44: Predicted and observed noise lev- Figure 45: Predicted and observed noise lev-els, 1/27/91, 0300, OBS 58 (2600 els, 1/27/91, 0600, OBS 58 (2500m), in dB re 1&Pa2/Hz. Observed m), in dB re Pa // -. O01,erve-spectrum is solid cm re. spectrum is sofid curve.
I00
2500mr, 1/27/91, 0900 2500 n, 3/04/91, 0400145 155
140- 150
135- 145
140-
~' 130 AS135-
o 125- I 130 ~aIIna
z 120- z 12
120-115-
115-
110 . 1
105 105'0 0.2 0.4 0.6 0 0.2 0.4 0.6
Frequency (Hz) Frequency (lHz)
Figure 46: Predicted and observed noise 1ev- Figure 47: Predicted and observed noise lev-els, 1/27/91, 0900, OBS 58 (2500 els, 3/04/91, 0400, OBS 58 (2500
min dB re tsPa2 /qz Obzc--cd ' ' PA2 IzOsrespectrum is solid curve, spectrum is solid curve.
101
2500 m, 3/04/91, 0600 2500 m, 3/04/91, 0800155 155
150, 150
145 145-
140- 140,* I I SI I I
135 ," 135 -
130 130s,Wi
5 125 " 125 z z120' 120
115- 115 ,
110 110
105 1050 0.2 0.4 0.6 0 0.2 0.4 0.6
Frequency (Hz) Frequency (Hz)
Figure 48: Predicted and observed noise lev- Figure 49: Predicted and observed noise lev-els, 3/04/91, 0600, OBS 58 (2500 els, 3/04/91, 0800, OBS 58 (2500m), in dB re pPa2 /Hs. Observed m), in dB re pPa2 /Hs. Observedspectrum Ib s,,'A*U curve, spectrum is solid curve.
102
2500 m, 3/04/91, 1000 2500 m,2/23/91, 0200155 A 145
I I
150-, ' 140
145-135
140
ca 130135" 0 12525- *
I3 ' '2
120
120"115 %
115
10 110-
105 105.0 0.2 0.4 0.6 0 0.2 0.4 0.6
Frequency (Hz) Frequency (Hz)
Figure 50: Predicted and observed noise lev- Figure 51: Predicted and observed noise lev-els, 3/04/91, 1000, OBS 58 (2500 els, 2/23/91, 0200, OBS 58 (2500m), in dB re pPa2/Hs. Observed m), in dB re IAPa?/Hs. Observedspectrum is solid curve, spectrum is solid curve.
103
2500 m, 2/23/91, 0300 2500 m, 2/23/91, 0400145 145
140 140
135 135,,. . i
* t
130) 130)
125 ,,'5 125-
I 0
z 120- z 120-
115 115
110 110
105' 1050 0.2 0.4 0.6 0 0.2 0.4 0.6
Frequency (Hz) Frequency (Hz)
Figure 52: Predicted and observed noise lev- Figure 53: Predicted and observed noise lev-els, 2/23/91, 0300, OBS 58 (2500 els, 2/23/91, 0400, OBS 58 (2500m), in dB re 1sPa2 /Hz. Observed m), in dB re uPa2 /Hs. Observedspectrum is solid curve, spectrum is solid curve.
104
2500 m, 2/23/91, 0500 2500 m, 2/23/91, 0600145 145
140 140
135- 135
S130 - 130-
125- ,0 125-;
0 0z 120- z 120";
115- 115 -
110- : 110-
105 1 ----- 10510 0.2 0.4 0.6 0 0.2 0.4 0.6
Frequency (Hz) Frequency (Hz)
Figure 54: Predicted and observed noise lev- Figure 55: Predicted and observed noise lev-els, 2/23/91, 0500, OBS 58 (2500 els, 2/23/gl, 0600, OBS 58 (2500m), in dB re uPa2/H. Observed m), in dB re pPa2/H. Observedspectrum is solid curve. spectrum is solid curve.
105
2500 m 1/27/91, 1500 2500 m, 1/27/91, 2100145 145
140 140
135 135-
I i " 130 " 130"
125- 125-
z 120 - 120,
115 115-
110 110
105, 1050 0.2 0.4 0.6 0 0.2 0.4 0.6
Frequency (Hz) Frequency (Hz)
Figure 56: Predicted and observed noise lev- Figure 57: Predicted and observed noise lev-els, 1/27/91, 1500, OBS 58 (2500 els, 1/27/91, 2100, OBS 58 (2500m), in dB re MPa 2/Hs. Observed m), in dB reuPa2/Hz. Observedspectrum is solid curve. spectrum is solid curve.
106